Related papers: Strong solution of 3D-NSE with exponential damping
We investigate the uniqueness of symmetric weak solutions to the stationary Navier-Stokes equation in a two-dimensional exterior domain $\Omega$. It is known that, under suitable symmetry condition on the domain and the data, the problem…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
Considering the stochastic Navier-Stokes system in $\mathbb{R}^d$ forced by a multiplicative white noise, we establish the local existence and uniqueness of the strong solution when the initial data take values in the critical space…
In this paper we are concerned with the 2D incompressible Navier-Stokes equations driven by space-time white noise. We establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions $u$ for…
In this paper, we establish the global existence and uniqueness of solution to $2$-D inhomogeneous incompressible Navier-Stokes equations \eqref{1.2} with initial data in the critical spaces. Precisely, under the assumption that the initial…
We consider the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. We prove the local existence and uniqueness of the strong solution in a…
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…
Whether the 3D incompressible Navier-Stokes equations will have a global smooth solution for all smooth, finite energy initial data is a Millennium Prize problem. One of the main difficulties of this problem is that the Navier-Stokes…
We consider the local well-posedness of strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with density containing vacuum initially. We first prove the local existence and uniqueness of…
We show the existence of (a class of) weak solutions to the three-dimensional stationary incompressible inhomogeneous Navier--Stokes equations with density-dependent viscosity coefficient in the axially symmetric case. Further symmetric…
We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution…
A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in 3 dimensions with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations…
The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data there exist infinitely many global in time weak solutions with…
In this paper, we study the connectedness and compactness of the attainability set of weak solutions to the three-dimensional Navier--Stokes equations with damping. Depending on the value of the parameter \b{eta}, which controls the damping…
We establish global well-posedness of strong solutions for the nonhomogeneous magnetohydrodynamic equations with density-dependent viscosity and initial density allowing vanish in two-dimensional (2D) bounded domains. Applying delicate…
We consider incompressible Navier-Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we…
Regularity properties of strong solutions are considered.
We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…
In this paper, we give two family of explicit blowup solution for $3$D incompressible Navier-Stokes equations in $\RR^3$. Here one family of solutions admit the smooth initial data, and the initial data of another family of solutions are…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…