Global existence of weak solutions to the incompressible Vlasov-Navier-Stokes system coupled to convection-diffusion equations

Time evolution of each profile, construction of an approximate solution In this section we shall construct an approximate solution to the Navier-Stokes equations by evolving in

Abstract This short note studies the problem of a global expansion of local results on existence of strong and classical solutions of Navier-Stokes equations in R 3..

In this paper, we investigate the time decay behavior to Lions weak solution of 2D incompressible density-dependent Navier-Stokes equations with variable viscosity..

When considering all the profiles having the same horizontal scale (1 here), the point is therefore to choose the smallest vertical scale (2 n here) and to write the decomposition

The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method

(2010) [2] we show that, in the case of periodic boundary conditions and for arbitrary space dimension d 2, there exist infinitely many global weak solutions to the

Keywords: Navier–Stokes equations; Uniqueness; Weak solution; Fourier localization; Losing derivative estimates.. In three dimensions, however, the question of regularity and

in Sobolev spaces of sufficiently high order, then we show the existence of a solution in a particular case and finally we solve the general case by using the