Seminar on nonlinear problems of PDE and mathematical physics on topic: “On properties of solutions of multidimensional Euler-Poisson equations in the repulsive case”
Speakers: Professor Rozanova O.S. ( M.V.Lomonosov State University, Moscow)
Title of the talk: Construction and justification of the asymptotics of fundamental solutions of parabolic equations
We show that there are no globally smooth nontrivial solutions of the Euler-Poisson equations, in particular, describing cold plasma oscillations, for physical dimensions 2 and 3 “in the general case”. The exceptions are radially symmetric affine solutions and those close to them, which are not localized. The non-physical dimension 4 is exceptional in the sense that axisymmetric solutions (apparently) preserve global smoothness for any initial data, and the oscillations here correspond to the Huygens pendulum. A natural question arises as to whether affine solutions retain smoothness if the requirement of axial symmetry is broken. It will be shown that the answer is negative.