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Seminar on partial differential equations

A class of global relatively smooth solutions for the Euler-Poisson system

Raphaël Danchin
Université Paris-Est Créteil


Tuesday, 15. December 2020 - 9:00 to 10:00

The lecture will be delivered on Zoom (only). The link to the seminar is:

Meeting ID: 989 1498 7846
Passcode: 889147

In this joint work with X. Blanc, B. Ducomet and Š. Nečasová (to appear in JHDE), we construct a class of global solutions to the Cauchy problem for the isentropic Euler equations coupled with the Poisson equation, in the whole space. The initial density is assumed to decay to 0 at infinity and the initial velocity is close to some reference velocity with Jacobian having positive spectrum bounded away from 0. By a suitable adaptation of Grassin-Serre’s work on the `pure’ compressible Euler equations, we obtain a global smooth solution  the large time behavior of which may be described in terms of some solution of the multi-dimensional Burgers equation. The stability of some special spherically symmetric stationary solution is also discussed.