Related papers: Nonlinear instability for the Navier-Stokes equati…

We study global existence and uniqueness of solutions to instationary inhomogeneous Navier-Stokes equations on bounded domains of $\R^n, n\geq 3$, with initial velocity in $B^0_{q,\infty}(\Om)$, $q\geq n$, and piecewise constant initial…

Building upon a recent work by two of the authours and J. Seidler on bw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an invariant measure to stochastic 2-D Navier-Stokes (with multiplicative…

The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…

We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonnegative density. In contrast with all the previous works on…

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…

We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…

It is shown that the incompressible Navier-Stokes equation can be derived from an infinite dimensional mean-field stochastic differential equation.

We show that a smooth linear unsteady velocity field $u(x,t)=A(t)x+f(t)$ solves the incompressible Navier--Stokes equation if and only if the matrix $A(t)$ has zero trace, and $\dot{{A}}(t)+A^{2}(t)$ is symmetric. In two dimensions, these…

We consider a system of nonlinear partial differential equations modeling the unsteady motion of an incompressible generalized Newtonian fluid with chemical reactions. The system consists of the generalized Navier-Stokes equations with…

This paper investigates the isentropic compressible Navier-Stokes equations on k-connected domains under Navier-slip boundary conditions. We study the multi-solvability of the stationary systems on general domains, which is closely related…

We address the local well-posedness for the stochastic Navier-Stokes system with multiplicative cylindrical noise in the whole space. More specifically, we prove that there exists a unique local strong solution to the system in…

This paper is concerned with nonlinear stability of viscous contact discontinuity to inflow problem for the one-dimensional full compressible Navier-Stokes equations with different ends in half space $[0,\infty)$. For the case when the…

We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of…

In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…

We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian.…

In this paper, we prove the global wellposedness of the Navier-Stokes equations describing a motion of compressible, viscous, barotropic fluid flow in a 3 dim. exterior domain in the $L_p$ in time and $L_2 \cap L_6$ maximal regularity…

This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that generic shear layers are nonlinearly unstable provided the…

We consider stability of non-rotating viscous gaseous stars modeled by the Navier-Stokes-Poisson system. Under general assumptions on the equations of states, we proved that the number of unstable modes for the linearized…

In this proceeding we expose a particular case of a recent result obtained by the authors regarding the incompressible Navier-Stokes equations in a smooth bounded and simply connected bounded domain, either in 2D or in 3D, with a Navier…

In this report, we study the long-time stability of the family of one-leg DLN methods for the two-dimensional incompressible Navier-Stokes equations. The family of DLN methods (with one parameter $\theta$), non-linear energy stable…