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Ping Zhang - One of the best experts on this subject based on the ideXlab platform.
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existence of incompressible and immiscible flows in critical function spaces on bounded domains
Journal of Mathematical Fluid Mechanics, 2019Co-Authors: Ping ZhangAbstract:We study global existence and uniqueness of solutions to inhomogeneous incompressible Navier–Stokes equations on bounded domains of $$\mathbb {R}^n, n\ge 2$$, with Initial Velocity in the Besov space $$B^0_{q,\infty }(\Omega )$$, $$q\ge n$$, and piecewise constant Initial density. Existence of solutions is proved when $$B^0_{n,\infty }$$-norm of Initial Velocity and Initial density difference are small, and for uniqueness we require that $$q>n$$. The proof of existence of solutions is done via an iterative scheme based on maximal $$L^\infty _\gamma $$-regularity of the Stokes operator in little Nicolskii spaces and on solvability for transport equations in the spaces of pointwise multipliers for little Nicolskii spaces, while the proof of uniqueness is done via a Lagrangian approach using the result of an time-evolutionary Stokes system with nonzero divergence obtained in this paper.
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inhomogeneous navier stokes equations in the half space with only bounded density
Journal of Functional Analysis, 2014Co-Authors: Raphael Danchin, Ping ZhangAbstract:Abstract In this paper, we establish the global existence and uniqueness of solutions to the inhomogeneous Navier–Stokes system in the half-space. The Initial density only has to be bounded and close enough to a positive constant, the Initial Velocity belongs to some critical Besov space, and the L ∞ norm of the inhomogeneity plus the critical norm to the horizontal components of the Initial Velocity has to be very small compared to the exponential of the norm to the vertical component of the Initial Velocity. With a little bit more regularity for the Initial Velocity, those solutions are proved to be unique. In the last section of the paper, our results are partially extended to the bounded domain case.
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well posedness of 3 d inhomogeneous navier stokes equations with highly oscillatory Initial Velocity field
Journal de Mathématiques Pures et Appliquées, 2013Co-Authors: Hammadi Abidi, Ping ZhangAbstract:Abstract Without smallness assumption on the variation of the Initial density function, we first prove the local well-posedness of 3-D incompressible inhomogeneous Navier–Stokes equations with Initial data ( a 0 , u 0 ) in the critical Besov spaces B λ , 1 3 λ ( R 3 ) × B ˙ p , 1 3 p − 1 ( R 3 ) for λ , p given by Theorem 1.1. Then we prove this system is globally well-posed provided that ‖ u 0 ‖ B ˙ p , 1 3 p − 1 is sufficiently small. In particular, this result implies the global well-posedness of 3-D inhomogeneous Navier–Stokes equations with highly oscillatory Initial Velocity field and any Initial density function with a positive lower bound.
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inhomogeneous navier stokes equations in the half space with only bounded density
arXiv: Analysis of PDEs, 2013Co-Authors: Raphael Danchin, Ping ZhangAbstract:In this paper, we establish the global existence of small solutions to the inhomogeneous Navier-Stokes system in the half-space. The Initial density only has to be bounded and close enough to a positive constant, and the Initial Velocity belongs to some critical Besov space. With a little bit more regularity for the Initial Velocity, those solutions are proved to be unique. In the last section of the paper, our results are partially extended to the bounded domain case.
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global well posedness of incompressible inhomogeneous fluid systems with bounded density or non lipschitz Velocity
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Jingchi Huang, Marius Paicu, Ping ZhangAbstract:In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier–Stokes equations with Initial data \({a_0 \in L^\infty (\mathbb{R}^d), u_0 = (u_0^h, u_0^d) \in \dot{B}^{-1+\frac{d}{p}}_{p, r} (\mathbb{R}^d)}\), which satisfy \({(\mu \| a_0 \|_{L^\infty} + \|u_0^h\|_{\dot{B}^{-1+\frac{d}{p}}_{p, r}}) {\rm exp}(C_r{\mu^{-2r}}\|u_0^d\|_{\dot{B}^{-1+\frac{d}{p}}_{p,r}}^{2r}) \leqq c_0\mu}\) for some positive constants c 0, C r and 1 < p < d, 1 < r < ∞. The regularity of the Initial Velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz Velocity fields. Furthermore, with additional regularity assumptions on the Initial Velocity or on the Initial density, we can also prove the uniqueness of such a solution. We should mention that the classical maximal L p (L q ) regularity theorem for the heat kernel plays an essential role in this context.
Jingchi Huang - One of the best experts on this subject based on the ideXlab platform.
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global well posedness of 3 d inhomogeneous navier stokes system with Initial Velocity being a small perturbation of 2 d solenoidal vector field
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Yuhui Chen, Jingchi HuangAbstract:Abstract Motivated by [21] , we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier–Stokes equations with large horizontal Velocity. In particular, we proved that when the Initial density is close enough to a positive constant, then given divergence free Initial Velocity field of the type ( v 0 h , 0 ) ( x h ) + ( w 0 h , w 0 3 ) ( x h , x 3 ) , we shall prove the global wellposedness of (1.1) . The main difficulty here lies in the fact that we will have to obtain the L 1 ( R + ; Lip ( R 3 ) ) estimate for convection Velocity in the transport equation of (1.1) . Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic Littlewood–Paley theory here.
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global well posedness of incompressible inhomogeneous fluid systems with bounded density or non lipschitz Velocity
Archive for Rational Mechanics and Analysis, 2013Co-Authors: Jingchi Huang, Marius Paicu, Ping ZhangAbstract:In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier–Stokes equations with Initial data \({a_0 \in L^\infty (\mathbb{R}^d), u_0 = (u_0^h, u_0^d) \in \dot{B}^{-1+\frac{d}{p}}_{p, r} (\mathbb{R}^d)}\), which satisfy \({(\mu \| a_0 \|_{L^\infty} + \|u_0^h\|_{\dot{B}^{-1+\frac{d}{p}}_{p, r}}) {\rm exp}(C_r{\mu^{-2r}}\|u_0^d\|_{\dot{B}^{-1+\frac{d}{p}}_{p,r}}^{2r}) \leqq c_0\mu}\) for some positive constants c 0, C r and 1 < p < d, 1 < r < ∞. The regularity of the Initial Velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz Velocity fields. Furthermore, with additional regularity assumptions on the Initial Velocity or on the Initial density, we can also prove the uniqueness of such a solution. We should mention that the classical maximal L p (L q ) regularity theorem for the heat kernel plays an essential role in this context.
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Global wellposdeness to incompressible inhomogeneous fluid system with bounded density and non-Lipschitz Velocity
2012Co-Authors: Jingchi Huang, Marius Paicu, Ping ZhangAbstract:In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with Initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The regularity of the Initial Velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz Velocity field. Furthermore, with additional regularity assumption on the Initial Velocity or on the Initial density, we can also prove the uniqueness of such solution. We should mention that the classical maximal regularity theorem for the heat kernel plays an essential role in this context.
Zhifei Zhang - One of the best experts on this subject based on the ideXlab platform.
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global well posedness for compressible navier stokes equations with highly oscillating Initial Velocity
Communications on Pure and Applied Mathematics, 2010Co-Authors: Qionglei Chen, Changxing Miao, Zhifei ZhangAbstract:In this paper, we prove global well-posedness for compressible Navier-Stokes equations in the critical functional framework with the Initial data close to a stable equilibrium. This result allows us to construct global solutions for the highly oscillating Initial Velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms. © 2010 Wiley Periodicals, Inc.
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global well posedness for the compressible navier stokes equations with the highly oscillating Initial Velocity
arXiv: Analysis of PDEs, 2009Co-Authors: Qionglei Chen, Changxing Miao, Zhifei ZhangAbstract:Cannone \cite{Cannone} proved the global well-posedness of the incompressible Navier-Stokes equations for a class of highly oscillating data. In this paper, we prove the global well-posedness for the compressible Navier-Stokes equations in the critical functional framework with the Initial data close to a stable equilibrium. Especially, this result allows us to construct global solutions for the highly oscillating Initial Velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms.
Michael Karas - One of the best experts on this subject based on the ideXlab platform.
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the Initial ion Velocity and its dependence on matrix analyte and preparation method in ultraviolet matrix assisted laser desorption ionization
Journal of Mass Spectrometry, 1999Co-Authors: Matthias Gluckmann, Michael KarasAbstract:Since the early days of matrix-assisted laser desorption/ionization (MALDI), measurements showing that MALDI ions and neutrals have high Initial velocities have led to wide acceptance of the idea that a jet of released material entrains analyte ions. The Initial Velocity, which could previously be determined only with large uncertainty, can be measured today with high reliability in a delayed-extraction MALDI/time-of-flight system by following the linear dependence of ion flight time vs the applied extraction delay. The detection of different Initial velocities for different matrices, with and without additives, for various preparation protocols and for different classes of analytes proves that the magnitude of the Initial Velocity can indeed be regarded as a valuable and meaningful characteristic of the MALDI process. Based on the results reported here, it is postulated that a high Initial Velocity results from incorporation of the analyte into the matrix crystals and that cooling upon expansion is effective at high Initial velocities and responsible for reduced fragmentation observed in such cases compared with ‘slow’ matrices. Copyright © 1999 John Wiley & Sons, Ltd.
S B Popov - One of the best experts on this subject based on the ideXlab platform.
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on the nature of the bimodal Initial Velocity distribution of neutron stars
Astronomy and Astrophysics, 2004Co-Authors: Ignazio Bombaci, S B PopovAbstract:We propose that the bimodal nature of the kick Velocity distribution of radio pulsars is connected to the dichotomy between hadronic stars (i.e. neutron stars with no quark matter content) and quark stars. Bimodality can appear due to different mechanisms of explosion which lead to the formation of two types of compact stars or due to two different sets of parameters driving a particular kick mechanism. The low Velocity maximum (at ∼100 km s −1 ) is associated with hadronic star formation, whereas the second peak corresponds to quark stars. In the model of delayed collapse of hadronic stars to quark stars (Berezhiani et al. 2003) quark deconfinement leads to a second energy release, and to a second kick, in addition to the kick imparted to the newly formed hadronic star during the supernova explosion. If the electromagnetic rocket mechanism can give a significant contribution to pulsar kicks, then the high Velocity peak can be associated with the shorter Initial spin periods of quark stars with respect to hadronic stars. We discuss these scenarios.
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on the nature of bimodal Initial Velocity distribution of neutron stars
arXiv: Astrophysics, 2004Co-Authors: Ignazio Bombaci, S B PopovAbstract:We propose that the bimodal nature of the kick Velocity distribution of radio pulsars is connected with the dichotomy between hadronic stars ({\it i.e.} neutron stars with no quark matter content) and quark stars. Bimodality can appear due to different mechanisms of explosion which leads to the formation of two types of compact stars or due to two different sets of parameters mastering a particular kick mechanism. The low Velocity maximum (at $\sim 100$ km s$^{-1}$) is connected with hadronic star formation, whereas the second peak corresponds to quark stars. In the model of delayed collapse of hadronic stars to quark stars (Berezhiani et al. 2003\nocite{bbd2003}) quark deconfinement leads to a second energy release, and to a second kick, in addition to the kick imparted to the newly formed hadronic star during the supernova explosion. If the electromagnetic rocket mechanism can give a significant contribution to pulsar kicks, then the high Velocity peak can be connected with the shorter Initial spin periods of quark stars with respect to hadronic stars. We discuss {\it pro et contra} of these scenarios.
