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Edriss S Titi - One of the best experts on this subject based on the ideXlab platform.
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global well posedness of the three dimensional primitive Equations with only horizontal viscosity and diffusion
Communications on Pure and Applied Mathematics, 2016Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:© 2015 Wiley Periodicals, Inc. In this paper, we consider the initial boundary value problem of the three-dimen-sional primitive Equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum Equations and only horizontal diffusion in the Temperature Equation. Global well-posedness of the strong solution is established for any H2 initial data. An N-dimensional logarithmic Sobolev embedding inequality, which bounds the L∞-norm in terms of the Lq-norms up to a logarithm of the Lp-norm for p>N of the first-order derivatives, and a system version of the classic Gronwall inequality are exploited to establish the required a priori H2 estimates for global regularity.
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global well posedness of strong solutions to a tropical climate model
Discrete and Continuous Dynamical Systems, 2016Co-Authors: Edriss S TitiAbstract:In this paper, we consider the Cauchy problem to the TROPIC CLIMATE MODEL derived by Frierson-Majda-Pauluis in [Comm. Math. Sci, Vol. 2 (2004)] which is a coupled system of the barotropic and the first baroclinic modes of the velocity and the typical midtropospheric Temperature. The system considered in this paper has viscosities in the momentum Equations, but no diffusivity in the Temperature Equation. We establish here the global well-posedness of strong solutions to this model. In proving the global existence of strong solutions, to overcome the difficulty caused by the absence of the diffusivity in the Temperature Equation, we introduce a new velocity $w$ (called the pseudo baroclinic velocity), which has more regularities than the original baroclinic mode of the velocity. An auxiliary function $\phi$, which looks like the effective viscous flux for the compressible Navier-Stokes Equations, is also introduced to obtain the $L^\infty$ bound of the Temperature. Regarding the uniqueness, we use the idea of performing suitable energy estimates at level one order lower than the natural basic energy estimates for the system.
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global well posedness of strong solutions to the 3d primitive Equations with horizontal eddy diffusivity
Journal of Differential Equations, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the 3D primitive Equations for oceanic and atmospheric dynamics with only horizontal diffusion in the Temperature Equation. Global well-posedness of strong solutions are established with H2 initial data. © 2014 Elsevier Inc. All rights reserved.
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global well posedness of the 3d primitive Equations with only horizontal viscosity and diffusion
arXiv: Analysis of PDEs, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the 3D primitive Equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum Equations and only horizontal diffusion in the Temperature Equation. Global well-posedness of strong solution is established for any $H^2$ initial data. An $N$-dimensional logarithmic Sobolev embedding inequality, which bounds the $L^\infty$ norm in terms of the $L^q$ norms up to a logarithm of the $L^p$-norm, for $p>N$, of the first order derivatives, and a system version of the classic Gronwall inequality are exploited to establish the required a priori $H^2$ estimates for the global regularity.
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local and global well posedness of strong solutions to the 3d primitive Equations with vertical eddy diffusivity
Archive for Rational Mechanics and Analysis, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the viscous 3D primitive Equations for oceanic and atmospheric dynamics with only vertical diffusion in the Temperature Equation. Local and global well-posedness of strong solutions are established for this system with H 2 initial data.
Erik Schnetter - One of the best experts on this subject based on the ideXlab platform.
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r process nucleosynthesis from three dimensional magnetorotational core collapse supernovae
The Astrophysical Journal, 2018Co-Authors: Philipp Mosta, Luke F Roberts, Goni Halevi, Christian D Ott, Jonas Lippuner, Roland Haas, Erik SchnetterAbstract:We investigate r-process nucleosynthesis in 3D general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-Temperature Equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are robust r-process sources only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of the order of 10^(13) G. Additionally, a comparison simulation that we restrict to axisymmetry results in overly optimistic r-process production for lower magnetic field strengths.
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r process nucleosynthesis from three dimensional magnetorotational core collapse supernovae
arXiv: High Energy Astrophysical Phenomena, 2017Co-Authors: Philipp Mosta, Luke F Roberts, Goni Halevi, Christian D Ott, Jonas Lippuner, Roland Haas, Erik SchnetterAbstract:We investigate r-process nucleosynthesis in three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-Temperature Equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are a robust r-process source only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of order $10^{13}$G. Additionally, a comparison simulation that we restrict to axisymmetry, results in overly optimistic r-process production for lower magnetic field strengths.
Chongsheng Cao - One of the best experts on this subject based on the ideXlab platform.
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global well posedness of the three dimensional primitive Equations with only horizontal viscosity and diffusion
Communications on Pure and Applied Mathematics, 2016Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:© 2015 Wiley Periodicals, Inc. In this paper, we consider the initial boundary value problem of the three-dimen-sional primitive Equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum Equations and only horizontal diffusion in the Temperature Equation. Global well-posedness of the strong solution is established for any H2 initial data. An N-dimensional logarithmic Sobolev embedding inequality, which bounds the L∞-norm in terms of the Lq-norms up to a logarithm of the Lp-norm for p>N of the first-order derivatives, and a system version of the classic Gronwall inequality are exploited to establish the required a priori H2 estimates for global regularity.
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global well posedness of strong solutions to the 3d primitive Equations with horizontal eddy diffusivity
Journal of Differential Equations, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the 3D primitive Equations for oceanic and atmospheric dynamics with only horizontal diffusion in the Temperature Equation. Global well-posedness of strong solutions are established with H2 initial data. © 2014 Elsevier Inc. All rights reserved.
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global well posedness of the 3d primitive Equations with only horizontal viscosity and diffusion
arXiv: Analysis of PDEs, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the 3D primitive Equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum Equations and only horizontal diffusion in the Temperature Equation. Global well-posedness of strong solution is established for any $H^2$ initial data. An $N$-dimensional logarithmic Sobolev embedding inequality, which bounds the $L^\infty$ norm in terms of the $L^q$ norms up to a logarithm of the $L^p$-norm, for $p>N$, of the first order derivatives, and a system version of the classic Gronwall inequality are exploited to establish the required a priori $H^2$ estimates for the global regularity.
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local and global well posedness of strong solutions to the 3d primitive Equations with vertical eddy diffusivity
Archive for Rational Mechanics and Analysis, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the viscous 3D primitive Equations for oceanic and atmospheric dynamics with only vertical diffusion in the Temperature Equation. Local and global well-posedness of strong solutions are established for this system with H 2 initial data.
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global well posedness of strong solutions to the 3d primitive Equations with horizontal eddy diffusivity
arXiv: Analysis of PDEs, 2014Co-Authors: Chongsheng Cao, Edriss S TitiAbstract:In this paper, we consider the initial-boundary value problem of the 3D primitive Equations for oceanic and atmospheric dynamics with only horizontal diffusion in the Temperature Equation. Global well-posedness of strong solutions are established with $H^2$ initial data.
Goni Halevi - One of the best experts on this subject based on the ideXlab platform.
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r process nucleosynthesis from three dimensional magnetorotational core collapse supernovae
The Astrophysical Journal, 2018Co-Authors: Philipp Mosta, Luke F Roberts, Goni Halevi, Christian D Ott, Jonas Lippuner, Roland Haas, Erik SchnetterAbstract:We investigate r-process nucleosynthesis in 3D general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-Temperature Equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are robust r-process sources only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of the order of 10^(13) G. Additionally, a comparison simulation that we restrict to axisymmetry results in overly optimistic r-process production for lower magnetic field strengths.
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r process nucleosynthesis from three dimensional magnetorotational core collapse supernovae
arXiv: High Energy Astrophysical Phenomena, 2017Co-Authors: Philipp Mosta, Luke F Roberts, Goni Halevi, Christian D Ott, Jonas Lippuner, Roland Haas, Erik SchnetterAbstract:We investigate r-process nucleosynthesis in three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-Temperature Equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are a robust r-process source only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of order $10^{13}$G. Additionally, a comparison simulation that we restrict to axisymmetry, results in overly optimistic r-process production for lower magnetic field strengths.
Christian D Ott - One of the best experts on this subject based on the ideXlab platform.
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r process nucleosynthesis from three dimensional magnetorotational core collapse supernovae
The Astrophysical Journal, 2018Co-Authors: Philipp Mosta, Luke F Roberts, Goni Halevi, Christian D Ott, Jonas Lippuner, Roland Haas, Erik SchnetterAbstract:We investigate r-process nucleosynthesis in 3D general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-Temperature Equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are robust r-process sources only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of the order of 10^(13) G. Additionally, a comparison simulation that we restrict to axisymmetry results in overly optimistic r-process production for lower magnetic field strengths.
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r process nucleosynthesis from three dimensional magnetorotational core collapse supernovae
arXiv: High Energy Astrophysical Phenomena, 2017Co-Authors: Philipp Mosta, Luke F Roberts, Goni Halevi, Christian D Ott, Jonas Lippuner, Roland Haas, Erik SchnetterAbstract:We investigate r-process nucleosynthesis in three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. The simulations include a microphysical finite-Temperature Equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission and absorption. We track the composition of the ejected material using the nuclear reaction network SkyNet. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae (CCSN) are important for their nucleosynthetic signature. We find that production of r-process material beyond the second peak is reduced by a factor of 100 when the magnetorotational jets produced by the rapidly rotating core undergo a kink instability. Our results indicate that 3D magnetorotationally powered CCSNe are a robust r-process source only if they are obtained by the collapse of cores with unrealistically large precollapse magnetic fields of order $10^{13}$G. Additionally, a comparison simulation that we restrict to axisymmetry, results in overly optimistic r-process production for lower magnetic field strengths.
