We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so called semigroup m...

to perhaps the fact that the turbulence model equations are solved only to obtain the eddy viscosity and also the Many researchers use a time-lagged or loosely coupled approach in solving the Navier–Stokes equations and two-equation turbuconvenience of simply adding separate routines to an exlence model equations in a time-marching method. The Navier– isting Navier–Stokes code. Consequently, ma...

We show that the two dimensional Navier–Stokes equations in the stream function and vorticity form with nonhomogeneous boundary conditions have a unique solution with a stream function having two space derivatives. 2005 Published by Elsevier Inc.

The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.

A discussion of recent numerical and algorithmic tools for the solution of certain flow problems arising in CFD, which are governed by the incompressible Navier-Stokes equations. The book contains the latest results for...

We consider Cauchy problem for three-dimensional Navier-Stokes system with periodic boundary conditions with initial data from the space of pseudo-measures Φ(α). We provide global existence and uniqueness of the solution for sufficiently small initial data.

We prove that every weak solution u to the 3D Navier-Stokes equation that belongs to the class L 3 L 9/2 and ∇u belongs to L 3 L 9/5 localy away from a 1/2-Hölder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.

We consider a special class of similarity solutions of the stationary Navier-Stokes equations and prove the existence of the solution for all the Reynolds numbers. We further prove that the solution exhibits interior and boundary layers as the Reynolds number tends to +1 and ?1, respectively.

We study boundary regularity of weak solutions of the Navier-Stokes equations in the half-space in dimension . We prove that a weak solution which is locally in the class with near boundary is Hölder continuous up to the boundary. Our main tool is a point-wise estimate for the fundamental solution of the Stokes system, which is of independent interest.