Construction of weak solutions to a pressureless viscous model driven by nonlocal attraction-repulsion


Maja Szlenk, University of Warsaw, Faculty of Mathematics, Informatics and Mechanics. 3 mai 2024 11:30 edp
Abstract:

The topic of the talk is existence of weak solutions to the pressureless Navier-Stokes system with nonlocal attraction--repulsion forces. We construct the solutions on the whole three-dimensional space, assuming that the viscosity coefficients are density-dependent. For the nonlocal term it is further assumed that the interaction kernel has the quadratic growth at infinity and almost quadratic singularity at zero. The main point of the construction is the derivation of the analogs of the Bresch--Desjardins and Mellet--Vasseur estimates in the nonlocal setting.