BZ Seminar in Analysis: Marcos Solera (University of Valencia)

Non-Uniqueness for the Forced 2D Euler and SQG Equations

In the 1960s, Yudovich established a fundamental result in the study of incompressible fluids: the global existence and uniqueness of solutions to the 2D Euler equation with vorticity in $L^1 \cap L^\infty$. Although in the 1980s DiPerna and Majda proved global existence in $L^1\cap L^p$ for $1<p<\infty$, the question of uniqueness in this range remained open until Vishik’s 2018 work, which demonstrated non-uniqueness in the presence of a forcing term. In this talk, we present a simpler proof of that result, based on an alternative construction of unstable vortices with compact support. Moreover, we extend the result to the supercritical Sobolev regime and to the SQG equation. This is joint work with A. Castro, D. Faraco and F. Mengual.</p>

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