A solution of 2D incompressible Euler equation with algebraic spiral roll-up in the presence of Wiener type perturbation

2023/11/28 by Jeon, Woohyu · 1 citation
#35Q31 #35Q35 #76B03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.16736

Abstract

Extending the results of Elling \citeElling-2013, Elling-2016, we construct a weak solution of 2D incompressible Euler equation with initial vorticity of the form w₀(x)=\vert x \vert^-1/μg(θ), where g ∈ L^p(\mathbbT) satisfies ∑_ℤ\vert n \vert^-0.5 \vert\widehatg(n)\vert < ∞. In particular, the solution is self-similar and shows algebraic spiral roll-up.

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• Homogeneous steady states for the generalized surface quasi-geostrophic equations

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