Damped Euler system with attractive Riesz interaction forces
The article focuses on the analysis of the barotropic Euler equation with additional linear damping in velocity and with pairwise attractive Riesz interactions, in particular, the momentum equation contains the term \(\lambda\rho \nabla \Lambda^{\alpha-d}(\rho - c)\) where \(\Lambda^s\) is defined as \((-\Delta)^{s/2}\). The whole problem is considered on a \(d\)-dimensional torus. The authors provide the global-in-time well-posedness result and, moroever, they specify the assumptions under which one can expect the exponential decay of the \(L^2\) norm of the solution.
scientific article; zbMATH DE number 7924870
scientific article