ﻻ يوجد ملخص باللغة العربية
We prove a weak stability result for the three-dimensional homogeneous incompressible Navier-Stokes system. More precisely, we investigate the following problem : if a sequence $(u_{0, n})_{nin N}$ of initial data, bounded in some scaling invariant space, converges weakly to an initial data $u_0$ which generates a global regular solution, does $u_{0, n}$ generate a global regular solution ? A positive answer in general to this question would imply global regularity for any data, through the following examples $u_{0,n} = n vf_0(ncdot)$ or $u_{0,n} = vf_0(cdot-x_n)$ with $|x_n|to infty$. We therefore introduce a new concept of weak convergence (rescaled weak convergence) under which we are able to give a positive answer. The proof relies on profile decompositions in anisotropic spaces and their propagation by the Navier-Stokes equations.
We prove that the energy equality holds for weak solutions of the 3D Navier-Stokes equations in the functional class $L^3([0,T);V^{5/6})$, where $V^{5/6}$ is the domain of the fractional power of the Stokes operator $A^{5/12}$.
In a previous work, we presented a class of initial data to the three dimensional, periodic, incompressible Navier-Stokes equations, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The aim of
In this article, we establish sufficient conditions for the regularity of solutions of Navier-Stokes equations based on one of the nine entries of the gradient tensor. We improve the recently results of C.S. Cao, E.S. Titi (Arch. Rational Mech.Anal.
The energy equalities of compressible Navier-Stokes equations with general pressure law and degenerate viscosities are studied. By using a unified approach, we give sufficient conditions on the regularity of weak solutions for these equalities to hol
Consider the anisotropic Navier-Stokes equations as well as the primitive equations. It is shown that the horizontal velocity of the solution to the anisotropic Navier-Stokes equations in a cylindrical domain of height $varepsilon $ with initial data