In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove ...

The derivation of the Navier-Stokes equation starting from the Liouville equation using projection techniques yields a friction term which is nonlinear in the velocity. Using the results of multilinear mode-coupling technique for calculating equlibrium correlation functions, it is shown that the secondorder part of the term is non-zero, thus leading to an incorrect formula for the equation.

Based on some geometrical considerations, we propose a two-step method to do digital image inpainting. In the first step, we try to propagate the isophote directions into the inpainting domain. An energy minimization model combined with the zero divergence condition is used to get a nonlinear Stokes equation. Once the isophote directions are constructed, an image is restored to fit the construc...

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. Appropriately scaled families solutions of discrete Boltzmann equation are shown to have fluctuations that locally in time converge strongly to a limit governed ...

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrodinger equation and an associated linear spectral problem ...

One shows that the Navier-Stokes equation in O⊂Rd, d = 2, 3, around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V (t, ξ) = ∑N i=1 Vi(t)ψi(ξ)β̇i(t), ξ ∈ O, where {βi}i=1 are independent Brownian motions and {ψi}i=1 is a system of functions on O with support in an arbitrary open subset O0 ⊂ O. The stochastic control input {Vi}i=1 is...