The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Song Jiang - One of the best experts on this subject based on the ideXlab platform.
-
low mach number limit of full navier stokes equations in a 3d Bounded Domain
2015Co-Authors: Changsheng Dou, Song JiangAbstract:Abstract This paper studies the low Mach number limit of the full compressible Navier–Stokes equations in a three-dimensional Bounded Domain where the velocity field and the temperature satisfy the slip boundary conditions and the Neumann boundary condition, respectively. The uniform estimates in the Mach number for the strong solutions are derived in a short time interval, provided that the initial density and temperature are close to the constant states and satisfy the “Bounded derivative conditions”. Thus the solutions of the full compressible Navier–Stokes equations converge to the one of the isentropic incompressible Navier–Stokes equations, as the Mach number vanishes.
-
on instability and stability of three dimensional gravity driven viscous flows in a Bounded Domain
2014Co-Authors: Fei Jiang, Song JiangAbstract:Abstract We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a Bounded Domain Ω of class C 2 . When the steady density is heavier with increasing height (i.e., the Rayleigh–Taylor steady-state), we show that the steady-state is linear unstable (i.e., the linear solution grows in time in H 2 ) by constructing a (standard) energy functional and exploiting the modified variational method. Then, by introducing a new energy functional and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard. When the steady density is lighter with increasing height, we show, with the help of a restricted condition imposed on steady density, that the steady-state is linearly globally stable and nonlinearly asymptotically stable in the sense of Hadamard.
-
on instability and stability of three dimensional gravity driven viscous flows in a Bounded Domain
2013Co-Authors: Fei Jiang, Song JiangAbstract:We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a Bounded Domain $\Omega$ of class $C^2$. When the steady density is heavier with increasing height (i.e., the Rayleigh-Taylor steady-state), we show that the steady-state is linear unstable (i.e., the linear solution grows in time in $H^2$) by constructing a (standard) energy functional and exploiting the modified variational method. Then, by introducing a new energy functional and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard. When the steady density is lighter with increasing height, we show, with the help of a restricted condition imposed on steady density, that the steady-state is linearly globally stable and nonlinearly locally stable in the sense of Hadamard.
-
On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a Bounded Domain
2013Co-Authors: Fei Jiang, Song Jiang, Dehua WangAbstract:Abstract We study the global existence of weak solutions to a multi-dimensional simplified Ericksen–Leslie system for compressible flows of nematic liquid crystals with large initial energy in a Bounded Domain Ω ⊂ R N , where N = 2 or 3 . By exploiting a maximum principle, Nirenbergʼs interpolation inequality and a smallness condition imposed on the N-th component of initial direction field d 0 to overcome the difficulties induced by the supercritical nonlinearity | ∇ d | 2 d in the equations of angular momentum, and then adapting a modified three-dimensional approximation scheme and the weak convergence arguments for the compressible Navier–Stokes equations, we establish the global existence of weak solutions to the initial-boundary problem with large initial energy and without any smallness condition on the initial density and velocity.
Nader Masmoudi - One of the best experts on this subject based on the ideXlab platform.
-
boundary layers and incompressible navier stokes fourier limit of the boltzmann equation in Bounded Domain i
2017Co-Authors: Ning Jiang, Nader MasmoudiAbstract:We establish the incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation with a general cutoff collision kernel in a Bounded Domain. Appropriately scaled families of DiPerna-Lions(-Mischler) renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number goes to 0. Every limit point is a weak solution to the Navier-Stokes-Fourier system with different types of boundary conditions depending on the ratio between the accommodation coefficient and the Knudsen number. The main new result of the paper is that this convergence is strong in the case of the Dirichlet boundary condition. Indeed, we prove that the acoustic waves are damped immediately; namely, they are damped in a boundary layer in time. This damping is due to the presence of viscous and kinetic boundary layers in space. As a consequence, we also justify the first correction to the infinitesimal Maxwellian that one obtains from the Chapman-Enskog expansion with Navier-Stokes scaling. This extends the work of Golse and Saint-Raymond [20,21] and Levermore and Masmoudi [28] to the case of a Bounded Domain. The case of a Bounded Domain was considered by Masmoudi and Saint-Raymond [34] for the linear Stokes-Fourier limit and Saint-Raymond [41] for the Navier-Stokes limit for hard potential kernels. Neither [34] nor [41] studied the damping of the acoustic waves. This paper extends the result of [34,41] to the nonlinear case and includes soft potential kernels. More importantly, for the Dirichlet boundary condition, this work strengthens the convergence so as to make the boundary layer visible. This answers an open problem proposed by Ukai [46]. © 2016 Wiley Periodicals, Inc.
-
Boundary layers and incompressible Navier-Stokes-Fourier limit of the Boltzmann Equation in Bounded Domain (I)
2015Co-Authors: Ning Jiang, Nader MasmoudiAbstract:We establish the incompressible Navier-Stokes-Fourier limit for solutions to the Boltzmann equation with a general cut-off collision kernel in a Bounded Domain. Appropriately scaled families of DiPerna-Lions-(Mischler) renormalized solutions with Maxwell reflection boundary conditions are shown to have fluctuations that converge as the Knudsen number goes to zero. Every limit point is a weak solution to the Navier-Stokes-Fourier system with different types of boundary conditions depending on the ratio between the accommodation coefficient and the Knudsen number. The main new result of the paper is that this convergence is strong in the case of Dirichlet boundary condition. Indeed, we prove that the acoustic waves are damped immediately, namely they are damped in a boundary layer in time. This damping is due to the presence of viscous and kinetic boundary layers in space. As a consequence, we also justify the first correction to the infinitesimal Maxwellian that one obtains from the Chapman-Enskog expansion with Navier-Stokes scaling. This extends the work of Golse and Saint-Raymond \cite{Go-Sai04, Go-Sai05} and Levermore and Masmoudi \cite{LM} to the case of a Bounded Domain. The case of a Bounded Domain was considered by Masmoudi and Saint-Raymond \cite{M-S} for linear Stokes-Fourier limit and Saint-Raymond \cite{SRM} for Navier-Stokes limit for hard potential kernels. Both \cite{M-S} and \cite{SRM} didn't study the damping of the acoustic waves. This paper extends the result of \cite{M-S} and \cite{SRM} to the nonlinear case and includes soft potential kernels. More importantly, for the Dirichlet boundary condition, this work strengthens the convergence so as to make the boundary layer visible. This answers an open problem proposed by Ukai \cite{Ukai}.
-
from the boltzmann equation to the stokes fourier system in a Bounded Domain
2003Co-Authors: Nader Masmoudi, Laure SaintraymondAbstract:We prove that the renormalized solutions of the Boltzmann equation considered in a Bounded Domain with different types of (kinetic) boundary conditions converge to the Stokes-Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a Bounded Domain. © 2003 Wiley Periodicals, Inc.
Laure Saintraymond - One of the best experts on this subject based on the ideXlab platform.
-
from the boltzmann equation to the stokes fourier system in a Bounded Domain
2003Co-Authors: Nader Masmoudi, Laure SaintraymondAbstract:We prove that the renormalized solutions of the Boltzmann equation considered in a Bounded Domain with different types of (kinetic) boundary conditions converge to the Stokes-Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a Bounded Domain. © 2003 Wiley Periodicals, Inc.
Fei Jiang - One of the best experts on this subject based on the ideXlab platform.
-
on instability and stability of three dimensional gravity driven viscous flows in a Bounded Domain
2014Co-Authors: Fei Jiang, Song JiangAbstract:Abstract We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a Bounded Domain Ω of class C 2 . When the steady density is heavier with increasing height (i.e., the Rayleigh–Taylor steady-state), we show that the steady-state is linear unstable (i.e., the linear solution grows in time in H 2 ) by constructing a (standard) energy functional and exploiting the modified variational method. Then, by introducing a new energy functional and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard. When the steady density is lighter with increasing height, we show, with the help of a restricted condition imposed on steady density, that the steady-state is linearly globally stable and nonlinearly asymptotically stable in the sense of Hadamard.
-
on instability and stability of three dimensional gravity driven viscous flows in a Bounded Domain
2013Co-Authors: Fei Jiang, Song JiangAbstract:We investigate the instability and stability of some steady-states of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a Bounded Domain $\Omega$ of class $C^2$. When the steady density is heavier with increasing height (i.e., the Rayleigh-Taylor steady-state), we show that the steady-state is linear unstable (i.e., the linear solution grows in time in $H^2$) by constructing a (standard) energy functional and exploiting the modified variational method. Then, by introducing a new energy functional and using a careful bootstrap argument, we further show that the steady-state is nonlinear unstable in the sense of Hadamard. When the steady density is lighter with increasing height, we show, with the help of a restricted condition imposed on steady density, that the steady-state is linearly globally stable and nonlinearly locally stable in the sense of Hadamard.
-
On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a Bounded Domain
2013Co-Authors: Fei Jiang, Song Jiang, Dehua WangAbstract:Abstract We study the global existence of weak solutions to a multi-dimensional simplified Ericksen–Leslie system for compressible flows of nematic liquid crystals with large initial energy in a Bounded Domain Ω ⊂ R N , where N = 2 or 3 . By exploiting a maximum principle, Nirenbergʼs interpolation inequality and a smallness condition imposed on the N-th component of initial direction field d 0 to overcome the difficulties induced by the supercritical nonlinearity | ∇ d | 2 d in the equations of angular momentum, and then adapting a modified three-dimensional approximation scheme and the weak convergence arguments for the compressible Navier–Stokes equations, we establish the global existence of weak solutions to the initial-boundary problem with large initial energy and without any smallness condition on the initial density and velocity.
Jishan Fan - One of the best experts on this subject based on the ideXlab platform.
-
regularity criteria for a ginzburg landau navier stokes in a Bounded Domain
2020Co-Authors: Jishan Fan, Zhaoyun Zhang, Yong ZhouAbstract:In this work, we prove some regularity criteria for a Ginzburg–Landau–Navier–Stokes system with the Coulomb gauge in a Bounded Domain $$\Omega \subset {\mathbb {R}}^3\,$$.
-
global strong solutions to the 3d full compressible navier stokes system with vacuum in a Bounded Domain
2018Co-Authors: Jishan FanAbstract:Abstract In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier–Stokes system with vacuum in a Bounded Domain Ω ⊂ R 3 by the bootstrap argument provided that the viscosity coefficients λ and μ satisfy that 7 λ > 9 μ and the initial data ρ 0 and u 0 satisfy that ‖ ρ 0 ‖ L ∞ ( Ω ) and ‖ ρ 0 | u 0 | 5 ‖ L 1 ( Ω ) are sufficiently small.
-
global strong solutions to the 3d full compressible navier stokes system with vacuum in a Bounded Domain
2017Co-Authors: Jishan FanAbstract:In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a Bounded Domain $\Omega\subset \mathbb{R}^3$ by the bootstrap argument provided that the viscosity coefficients $\lambda$ and $\mu$ satisfy that $7\lambda>9\mu$ and the initial data $\rho_0$ and $u_0$ satisfy that $\|\rho_0\|_{L^\infty(\Omega)}$ and $\|\rho_0|u_0|^5\|_{L^1(\Omega)}$ are sufficient small.
-
uniform well posedness and singular limits of the isentropic navier stokes maxwell system in a Bounded Domain
2015Co-Authors: Jishan Fan, Gen NakamuraAbstract:We prove the global-in-time and uniform-in-\({(\epsilon_1,\epsilon_2)}\) of strong solutions to the isentropic Navier–Stokes–Maxwell system in a Bounded Domain, when \({\epsilon_1}\) is the Mach number, and \({\epsilon_2}\) is the dielectric constant. Consequently, we obtain the convergences of compressible Navier–Stokes–Maxwell system to the incompressible Navier–Stokes–Maxwell system (\({\epsilon_1\rightarrow 0}\) and \({\epsilon_2}\) fixed), the compressible magnetohydrodynamic equations (\({\epsilon_1}\) fixed and \({\epsilon_2\rightarrow 0}\)) or the incompressible magnetohydrodynamic equations (\({\epsilon_1\rightarrow 0}\) and \({\epsilon_2\rightarrow 0}\)) for well-prepared data.
-
blow up criteria of smooth solutions to the 3d boussinesq system with zero viscosity in a Bounded Domain
2012Co-Authors: Jishan Fan, Gen Nakamura, Haibing WangAbstract:Abstract We prove that a smooth solution of the 3D Boussinesq system with zero viscosity in a Bounded Domain breaks down, if a certain norm of vorticity blows up at the same time. Here this norm is weaker than the bmo-norm.