相关论文: Well-posedness in critical spaces for the compress…

The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work…

We prove the global well-posedness of three dimensional compressible Navier-Stokes equations for some classes of large initial data, which is of large oscillation for the density and large energy for the velocity. The structure of the…

We address the local well-posedness of the hydrostatic Navier-Stokes equations. These equations, sometimes called reduced Navier-Stokes/Prandtl, appear as a formal limit of the Navier-Stokes system in thin domains, under certain constraints…

We are concerned with the barotropic compressible Navier-Stokes equations on the real line. Our primary goal is to establish the global well-posedness in a critical regularity framework in the case where the initial data are small…

We consider a free boundary problem of the Navier--Stokes equations in the three-dimensional Euclidean space with moving contact line, where the 90$^\circ$-contact angle condition is posed. We show that for given $T > 0$ the problem is…

In this paper, we mainly study the Cauchy problem for the full compressible Navier-Stokes equations in Sobolev spaces. We establish the global well-posedness of the equations with small initial data by using Friedrich's method and…

We prove the ill-posedness of the 3-D baratropic Navier-Stokes equation for the initial density and velocity belonging to the critical Besov space $(\dot{B}^{\f 3p}_{p,1}+\bar{\rho},\,\dot{B}^{\f 3p-1}_{p,1})$ for $p>6$ in the sense that a…

In this paper, the initial-boundary value problem of the 1D full compressible Navier-Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any $H^1$ initial…

We study the Cauchy problem in $n$-dimensional space for the system of Navier-Stokes equations in critical mixed-norm Lebesgue spaces. Local well-posedness and global well-posedness of solutions are established in the class of critical…

This work is the continuation of the recent paper \cite{D2} devoted to the density-dependent incompressible Euler equations. Here we concentrate on the well-posedness issue in Besov spaces of type $B^s_{\infty,r}$ embedded in the set of…

In this paper, we consider the local well-posedness of the Prandtl boundary layer equations that describe the behavior of boundary layer in the small viscosity limit of the compressible isentropic Navier-Stokes equations with non-slip…

This paper presents a new approach to the local well-posedness of the $1d$ compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the $1d$ parabolic…

In this paper, we study local well-posedness for the Navier-Stokes equations (NSE) with the arbitrary initial value in homogeneous Sobolev-Lorentz spaces $\dot{H}^s_{L^{q, r}}(\mathbb{R}^d):= (-\Delta)^{-s/2}L^{q,r}$ for $d \geq 2, q > 1, s…

In this paper, we prove the local well-posedness of 3-D density-dependent liquid crystal flows with initial data in the critical Besov spaces, without assumptions of small density variation. Furthermore, if the initial density is close…

We establish the local in time well-posedness of strong solutions to the vacuum free boundary problem of the compressible Navier-Stokes-Poisson system in the spherically symmetric and isentropic motion. Our result captures the physical…

In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…

In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with on-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant…

We investigate the barotropic compressible Navier-Stokes equations with the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial density that is allowed to vanish, we establish the global…

We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $\mathbb{R}^d$ (with $d\geq2$). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global…

In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility…