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On threshold phenomena for the Euler-Poisson equations

O. S. Rozanova

Lomonosov Moscow State University



Abstract: It is proved that the radially symmetric solutions of the repulsive Euler-Poisson equations with a non-zero background, corresponding to cold plasma oscillations, blow up in many spatial dimensions for almost all initial data. Moreover, if a solution is globally smooth in time, then it is either affine or tends to affine as $t\to\infty$. This behavior is strikingly different from the behavior of solutions of the Euler-Poisson equations with zero background, as well as solutions of "attractive" Euler-Poisson equations with a non-zero background, where the initial data is divided into two sets of non-zero measure, one of which corresponds to globally smooth solutions.

Website: https://teams.microsoft.com/l/meetup-join/19%3ameeting_YzMyMjgxMjktYTY5ZC00M2Y4LWIzYTgtNDVjNTMxZTM1Njhh%40thread.v2/0?context=%7b%22Tid%22%3a%222ae95c20-c675-4c48-88d3-f276b762bf52%22%2c%22Oid%22%3a%2266c4b047-af30-41c8-9097-2039bac83cbc%22%7d


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