Related papers: Inviscid Large deviation principle and the 2D Navi…
The main objective of this paper is to demonstrate the uniform large deviation principle (UDLP) for the solutions of two-dimensional stochastic Navier-Stokes equations (SNSE) in the vorticity form when perturbed by two distinct types of…
We prove the existence and uniqueness of weak solutions of the inhomogeneous incompressible Navier--Stokes equations without vacuum using the relative energy method. We present a novel and direct proof of the existence of weak solutions…
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…
We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in $L^p$…
We consider the incompressible 2D Navier-Stokes equations with periodic boundary conditions driven by a deterministic time periodic forcing and a degenerate stochastic forcing. We show that the system possesses a unique ergodic periodic…
The paper concerns with the global well-posedness issue of the 2D incompressible inhomogeneous Navier-Stokes (INS) equations with fractional dissipation and rough density. We first establish the $L^q_t(L^p)$-maximal regularity estimate for…
In this paper, we first prove the local well-posedness of the 2-D incompressible Navier-Stokes equations with variable viscosity in critical Besov spaces with negative regularity indices, without smallness assumption on the variation of the…
In this paper, we first construct a class of global strong solutions for the 2-D inhomogeneous Navier-Stokes equations under very general assumption that the initial density is only bounded and the initial velocity is in…
In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Levy noise with periodic boundary conditions. Then we establish the large deviation principles…
In this work we study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and in particular, we confirm at the nonlinear level the qualitative behavior predicted by Kelvin's 1887 linear analysis.…
We prove the existence and some moment estimates for an invariant measure $\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\mathbb R^2$ and with highly regular initial data. The result is achieved…
We establish uniform bounds and the inviscid limit in $L^p$-based Sobolev conormal spaces for the solutions of the Navier-Stokes equations with the Navier boundary conditions in the half-space. We extend the vanishing viscosity results…
In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional…
We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…
We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal…
We study the effects of weak viscosity on shock formation in 1D hyperbolic conservation laws. Given an inviscid solution that forms a nondegenerate shock, we add a small viscous regularization and study the limit as the viscosity vanishes.…
We study the large deviations principle (LDP) of Donsker-Varadhan type for the white-forced Navier-Stokes system in a bounded domain. Under the assumption that the noise is non-degenerate, we establish level-2 and level-3 LDPs with rate…
We prove uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We make use of the Lagrangean framework in comparing the instantaneous states of corresponding fluid particles in two…
Navier-Stokes equations in the whole space R^3 subject to an anisotropic viscosity and a random perturbation of multiplicative type is described. By adding a term of Brinkman-Forchheimer type to the model, existence and uniqueness of global…
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…