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In this paper, we are concerned with the global wellposedness of 3-D inhomogeneous incompressible Navier-Stokes equations \eqref{1.3} in the critical Besov spaces with the norm of which are invariant by the scaling of the equations and…

Analysis of PDEs · Mathematics 2013-01-29 Jean-Yves Chemin , Marius Paicu , Ping Zhang

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space under some admissible condition. The result…

Analysis of PDEs · Mathematics 2023-10-17 Yuan Cai , Bin Han , Na Zhao

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near…

Analysis of PDEs · Mathematics 2009-11-13 Zhen Lei , Chun Liu , Yi Zhou

This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…

Analysis of PDEs · Mathematics 2022-08-08 Xinghong Pan , Jiang Xu

In this paper we obtain a result about the global existence of weak solutions for the $d$-dimensional Bussinesq system, with viscosity dependent on temperature. The initial temperature is just supposed to be bounded, while the initial…

Analysis of PDEs · Mathematics 2015-11-03 Francesco De Anna

The global existence of classical solutions to the 3D compressible magneto-micropolar fluid system without resistivity and spin viscosity in a strip domain was recently established by Feng, Hong, and Zhu [Sci. China Math., 2024]. While Lin…

Analysis of PDEs · Mathematics 2026-05-22 Youyi Zhao

This paper is dedicated to the study of both viscous compressible barotropic fluids and Navier-Stokes equation with dependent density, when the viscosity coefficients are variable, in dimension $d\geq2$. We aim at proving the local and…

Analysis of PDEs · Mathematics 2011-07-13 Frédéric Charve , Boris Haspot

It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…

Fluid Dynamics · Physics 2023-06-14 F. Lam

In this paper, we study the global well-posedness of the 2D compressible Navier-Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\l$ is the…

Analysis of PDEs · Mathematics 2012-02-08 Quansen Jiu , Yi Wang , Zhouping Xin

This work investigates the existence and uniqueness of local weak solutions for the d-dimensional $(d \geq 2)$ fractional magnetic B\'enard system without thermal diffusion, integrating the B\'enard equation and MHD system. For $\kappa = 0$…

Analysis of PDEs · Mathematics 2024-09-27 Anis Rahmani , Abdelaziz Mennouni

We are concerned with global existence of regular solutions to full compressible Navier-Stokes equations and their asymptotic behavior when the Mach number is sufficiently small. We establish global existence in critical Besov spaces for…

Analysis of PDEs · Mathematics 2026-03-03 Sai Li

In this paper we study the initial-boundary value problem for the magnetohydrodynamic system in three dimensional exterior domain. We show an existence theorem of global in time strong solution for small initial data and we also show its…

Analysis of PDEs · Mathematics 2016-09-07 Norikazu Yamaguchi

In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure: $u_0=u_0^r e_r+\ut_0 e_\theta+u_0^z e_z, ~b_0=b_0^\theta e_\theta.$ We prove that, this system is global well-posed…

Analysis of PDEs · Mathematics 2017-05-22 Yanlin Liu

The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic…

Analysis of PDEs · Mathematics 2015-10-26 Song Jiang , Fucai Li

We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic viscous and non-resistive magnetohydrodynamic flows. The global well-posedness of strong solutions with general large data is…

Analysis of PDEs · Mathematics 2015-05-15 Song Jiang , Jianwen Zhang

We are concerned with an initial boundary value problem for the compressible magnetohydrodynamic equations with viscosity depending on the density. It is show that for the initial density away from vacuum, the strong solution to the problem…

Analysis of PDEs · Mathematics 2016-04-01 Xin Zhong

We prove the existence and uniqueness of weak solutions of the three dimensional compressible magnetohydrodynamics (MHD) equations. We first obtain the existence of weak solutions with small $L^2$-norm which may display codimension-one…

Analysis of PDEs · Mathematics 2020-11-12 Anthony Suen

In this paper, we study the Cauchy problem of the isentropic compressible magnetohydrodynamic equations in $\mathbb{R}^{3}$. When $(\gamma-1)^{\frac{1}{6}}E_{0}^{\frac{1}{2}}$, together with the $\|H_{0}\|_{L^{2}}$, is suitably small, a…

Analysis of PDEs · Mathematics 2015-03-12 Guangyi Hong , Xiaofeng Hou , Hongyun Peng , Changjiang Zhu

In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum…

Analysis of PDEs · Mathematics 2018-06-07 Edriss S. Titi , Saber Trabelsi

This paper concerns the Cauchy problem of the nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact…

Analysis of PDEs · Mathematics 2015-06-17 Boqiang Lv , Zhonghai Xu , Xin Zhong