Related papers: Asymptotic stability of Landau solutions to Navier…
In this paper, we mainly consider global well-posedness and long time behavior of compressible Navier-Stokes equations without heat conduction in $L^p$-framework. This is a generalization of Peng and Zhai \cite{peng}(SIMA, 55(2023), no.2,…
We study existence and stability of steady solutions of the isentropic compressible Navier-Stokes equations on a finite interval with non characteristic boundary conditions, for general not necessarily small-amplitude data. We show that…
One proves the existence and uniqueness in $(L^p(\mathbb{R}^3))^3$, $\frac{3}{2}<p<2$, of a global mild solution to random vorticity equations associated to stochastic $3D$ Navier-Stokes equations with linear multiplicative Gaussian noise…
This work studies the system of $3D$ stationary Navier-Stokes equations. Several Liouville type theorems are established for solutions in mixed-norm Lebesgue spaces and weighted mixed-norm Lebesgue spaces. In particular, we show that, under…
We prove the nonlinear time-asymptotic stability of the composite wave consisting of a planar rarefaction wave and a planar viscous shock for the three-dimensional (3D) compressible barotropic Navier-Stokes equations under generic…
In this paper, we establish Liouville-type theorems for the steady compressible Navier-Stokes system. Assuming a smooth solution \(u \in L^p(\mathbb{R}^3)\), \(3 \le p \le \frac{9}{2}\), with bounded density, one obtains \(u \equiv0\). This…
This paper investigates the time asymptotic stability of composite waves formed by two shock waves within the context of one-dimensional relaxed compressible Navier-Stokes equations. We demonstrate that the composite waves consisting of two…
In this paper we consider classes of initial data that ensure local-in-time Hadamard well-posedness of the associated weak Leray-Hopf solutions of the three-dimensional Navier-Stokes equations. In particular, for any solenodial $L_{2}$…
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…
In this work we consider the Keller-Segel system coupled with Navier-Stokes equations in $\mathbb{R}^{N}$ for $N\geq2$. We prove the global well-posedness with small initial data in Besov-Morrey spaces. Our initial data class extends…
In 1944 L.D.Landau calculated a very interesting family of explicit solutions of the steady-state 3d Navier-Stokes equations. The solutions are derived under certain assumptions of symmetry, which reduce the Navier-Stokes equations to a…
We prove the unique existence of solutions of the 3D incompressible Navier-Stokes equations in an exterior domain with small non-decaying boundary data, for $t \in R$ or $t \in (0,\infty)$. In the latter case it is coupled with small…
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…
In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases.…
In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is…
We study the asymptotic stability of a planar rarefaction wave (in the $ x_1 $- direction) for the 3-d isentropic Navier-Stokes equations, where the initial perturbation is periodic on the torus $ \mathbb{T}^3 $ with zero average. To solve…
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…
In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system provided that the vertical viscous coefficient of the system is sufficiently large compared to some critical norm of the initial data. Then we…
In this paper, we first consider global well-posedness and long time behavior of compressible Navier-Stokes equations with Yukawa-type potential in $L^p$-framework under the stability condition $P'(\bar\rho)+\gamma\bar\rho>0$. Here…
In this paper, we investigate the well-posedness and ill-posedness issues for the incompressible stationary Hall-magnetohydrodynamic (Hall-MHD) system in $\mathbb{R}^3.$ We first show the existence and uniqueness of solutions provided with…