Wild solutions to isentropic Euler equations starting from smooth initial data
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题目: Wild solutions to isentropic Euler equations starting from smooth initial data
报告人: Ondrej Kreml，Institute of Mathematics，Academic of Science，Czech Republic
摘要: We consider the isentropic Euler equations of gas dynamics in
the whole two-dimensional space and we prove the existence of a smooth initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant T > 0. In order to continue the solution after the formation of the discontinuity, we adjust and apply the L^\infty theory developed by De Lellis and Szekelyhidi and we construct infinitely many solutions.This is a joint work with E. Chiodaroli, V. Macha and S. Schwarzacher.