Related papers: Global large solutions to 3-D inhomogeneous Navier…

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…

In this paper, we are concerned with the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space…

Without any smallness assumption, we prove the global unique solvability of the 2-D incompressible inhomogeneous Navier-Stokes equations with initial data in the critical Besov space, which is almost the energy space in the sense that they…

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces,…

In this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\ge2$. In order to better reflect the characteristics of the dispersion equation, we make…

This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data…

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

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…

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants,…

The issue of global well-posedness for the 3D inhomogenous incompressible Navier-Stokes equations was first addressed by Kazhikov in 1974. In this manuscript, we obtain its global well-posedness for the system with density-dependent…

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…

In this article, we consider the global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity. More precisely, assuming $a_0 \in \dot{B}_{q,1}^{\frac{3}{q}}(\mathbb{R}^3)$ and…

In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier-Stokes equations with ill-prepared large initial data which are slowly varying in one space variable, that is, initial data of the form…

We investigate the global unique Fujita-Kato solution to the 3-D inhomogeneous incompressible Navier-Stokes equations with initial velocity $u_0$ being sufficiently small in critical spaces and with initial density being bounded from above…

In this paper, we study the global well-posedness of the 3-D inhomogeneous incompressible Navier-Stokes system (INS in short) with initial density $\rho_0$ being discontinuous and initial velocity $u_0$ belonging to some critical space.…

In this paper we consider the incompressible inhomogeneous Navier-Stokes equations in the whole space with dimension $n\geq 3$. We present local and global well-posedness results in a new framework for inhomogeneous fluids, namely…

In this paper we obtain new well-possedness results concerning a linear inhomogenous Stokes-like system. These results are used to establish local well-posedness in the critical spaces for initial density $\rho_{0}$ and velocity $u_{0}$…

Given solenoidal vector $u_0\in H^{-2\d}\cap H^1(\R^2),$ $\r_0-1\in L^2(\R^2),$ and $\r_0 \in L^\infty\cap\dot{W}^{1,r}(\R^2)$ with a positive lower bound for $\d\in (0,\f12)$ and $2<r<\f{2}{1-2\d},$ we prove that 2-D incompressible…

We investigate the local wellposedness of incompressible inhomogeneous Navier-Stokes equations on the Torus $\T^3$, with initial data in the critical Besov spaces. Under some smallness assumption on the velocity in the critical space…

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…