Related papers: Pressure Regularity Criterion for the Three-dimens…
A three-dimensional chemotaxis-Navier-Stokes system is considered. It is known that for all suitably regular initial data, a corresponding initial-boundary value problem admits at least one global weak solution which can be obtained as the…
Stochastic Navier--Stokes equations in a thin three-dimensional domain are considered, driven by additive noise. The convergence of martingale solution of the stochastic Navier--Stokes equations in a thin three-dimensional domain to the…
We establish several boundary $\varepsilon$-regularity criteria for suitable weak solutions for the 3D incompressible Navier-Stokes equations in a half cylinder with the Dirichlet boundary condition on the flat boundary. Our proofs are…
We prove the time-asymptotic stability toward planar rarefaction wave for the three-dimensional full compressible Navier-Stokes equations in an infinite long flat nozzle domain $\mathbb{R}\times\mathbb{T}^2$. Compared with one-dimensional…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
We consider the motion of incompressible viscous non-homogeneous fluid described by the Navier-Stokes equations in a bounded cylinder under boundary slip conditions. Assume that the third co-ordinate axis is the axis of the cylinder.…
The global regularity for the incompressible magnetohydrodynamic equations (MHD) in three dimensions is a long standing open problem of fluid dynamics and PDE theory. The Navier-Stokes equations can be viewed as a special case of MHD with a…
This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a…
We establish the existence of a uniformly bounded $ C^\infty $ solution of the Navier-Stokes equations on $\mathbb{R}^3 x\ [0, \infty) $ without external forces or boundaries for a divergence free initial condition $ u_o \in \cap_m H^m $…
In this paper, we consider the forced incompressible Navier-Stokes equations with vanishing viscosity on the three-dimensional torus. We show that there are (classical) solutions for which the dissipation rate of the kinetic energy is…
In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…
In this paper, we investigate the 3D inhomogeneous Navier-Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution $(\rho, \mathbf{u})$ satisfies suitable conditions.
The paper is devoted to studying controllability properties for 3D Navier-Stokes equations in a bounded domain. We establish a sufficient condition under which the problem in question is exactly controllable in any finite-dimensional…
We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…
In this paper, we consider the conditional regularity of weak solution to the 3D Navier--Stokes equations. More precisely, we prove that if one directional derivative of velocity, say $\partial_3 u,$ satisfies $\partial_3 u \in…
In this paper, we consider the regularity criterion for 3D incompressible Navier-Stokes equations in terms of one directional derivative of the velocity in anisotropic Lebesgue spaces. More precisely, it is proved that u becomes a regular…
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…
We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissipation and which enjoy uniform bounds in the space $L_t^3…