Related papers: On the anisotropic hyperdissipative Navier-Stokes …
In this paper, we consider the model of 3D incompressible Navier-Stokes equations and 2D supercritical Surface Quasi-Geostrophic equations with time oscillation in the nonlinear term. We obtain that there exists global smooth solution of…
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are…
We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-dependent viscosity and large external force. Under a general assumption on the density-dependent viscosity, we prove that…
In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients and a term of capillarity introduced by Coquel et al in \cite{5CR}. This model includes at the same time the barotropic…
The problem of global-in-time regularity for the 3D Navier-Stokes equations, i.e., the question of whether a smooth flow can exhibit spontaneous formation of singularities, is a fundamental open problem in mathematical physics. Due to the…
We prove that for initial data of the form \begin{equation}\nonumber u_0^\epsilon(x) = (v_0^h(x_\epsilon), \epsilon^{-1}v_0^n(x_\epsilon))^T,\quad x_\epsilon = (x_h, \epsilon x_n)^T, n \geq 4, \end{equation} the Cauchy problem of the…
We study the Cauchy problem for the incompressible Navier-Stokes equation \begin{align} u_t -\Delta u+u\cdot \nabla u +\nabla p=0, \ \ {\rm div} u=0, \ \ u(0,x)= \delta u_0. \label{NS} \end{align} For arbitrarily small $\delta>0$, we show…
We consider the Cauchy problem for the full compressible Navier-Stokes equations with vanishing of density at infinity in R3. Our main purpose is to prove the existence (and uniqueness) of global strong and classical solutions and study the…
We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…
In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…
This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
This paper studies the incompressible limit of global strong solutions to the three-dimensional compressible Navier-Stokes equations associated with Navier's slip boundary condition, provided that the time derivatives, up to first order, of…
A fundamental problem in analysis is to decide whether a smooth solution exists for the Navier-Stokes equations in three dimensions. In this paper we shall study this problem. The Navier-Stokes equations are given by:…
In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for 3D incompressible Navier-Stokes-Cahn-Hilliard equations. First, using Banach fixed point theorem, we establish the local well-posedness of…
We study the anisotropic, incompressible Cahn-Hilliard-Navier-Stokes system with variable density in a bounded smooth domain $\Omega \subset \mathbb{R}^d$. This work extends previous results on the isotropic case by incorporating…
This paper is devoted to the study of the Cauchy problem for the stratified Navier-Stokes system in space dimension three. In the first part of the paper, we prove the existence of a unique global solution $(v_\nu,\rho_\nu)$ for this system…
This paper concerns the Cauchy problem in R^d for the stochastic Navier-Stokes equation \partial_tu=\Delta u-(u,\nabla)u-\nabla p+f(u)+ [(\sigma,\nabla)u-\nabla \tilde p+g(u)]\circ \dot W, u(0)=u_0,\qquad divu=0, driven by white noise \dot…