arXiv subjects

Vladimir Chepyzhov

Publications and source records attributed to Vladimir Chepyzhov.

2 recordsLinked to original sources

arXiv2017

Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions

We consider the damped and driven Navier--Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain $Ω\subset\mathbf{R}^2$. We show that the damped Euler system has a (strong) global attractor in~$H^1(Ω)$. We also show that in the vanishing viscosity limit the global attractors of the Navier--Stokes system converge in the non-symmetric Hausdorff distance in $H^1(Ω)$ to the the strong global attractor of the limiting damped Euler system (whose solutions are not necessarily unique).

math.AP↗

arXiv2015

Infinite energy solutions for Dissipative Euler equations in R^2

We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the further development of the weighted energy theory for the Navier-Stokes and Euler type problems. In addition, the existence of weak locally compact global attractor is proved and some extra compactness of this attractor is obtained.

math.AP↗