Non-uniqueness of admissible solutions for the 2D Euler equation with $L^p$ vortex data

Francisco Mengual

For any $2<p<\infty$ we prove that there exists an initial velocity field $v^{\circ }\in L^2$ with vorticity ${\omega }^{\circ }\in L^1\cap L^p$ for which there are infinitely many bounded admis…