Velocity blow-up in $C^1\cap H^2$ for the 2D Euler equations

Junha Kim; Min Jun Jo

Velocity blow-up in $C^1\cap H^2$ for the 2D Euler equations

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arxiv 2211.13872 v1 pith:GCFGAJT2 submitted 2022-11-25 math.AP

Min Jun Jo , Junha Kim This is my paper · ORCID

classification math.AP

keywords equationseulerblow-upconstructionescapesgiveillposednessinstantaneously

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abstract

We give a vorticity-dynamical proof of $C^1\cap H^2$-illposedness of the 2D Euler equations. Our construction shows that the unique Yudovich solution escapes both $C^1$ and $H^2$ instantaneously.

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Global well-posedness for the incompressible Euler equations in an endpoint Sobolev space
math.AP 2026-07 conditional novelty 7.0 of 10

The 2D Euler vorticity equation is shown to be globally well-posed in the endpoint Sobolev space W^{2,1}, and the 3D axisymmetric no-swirl case in W^{3,1}, closing the p=1 endpoint of the critical Sobolev scale.

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