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arXiv · 2410.19057

Continuity of the solution map of some active scalar equations in H\"older and Zygmund spaces

Marc Magaña
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Abstract

We prove that the solution map for a family of non-linear transport equations in $\mathbb{R}^n$, with a velocity field given by the convolution of the density with a kernel that is smooth away from the origin and homogeneous of degree $-(n-1)$, is continuous in both the little H\"older class and the little Zygmund class. For particular choices of the kernel, one recovers well-known equations such as the 2D Euler or the 3D quasi-geostrophic equations.

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Marc Magaña. 2024-10-24. Continuity of the solution map of some active scalar equations in H\"older and Zygmund spaces. https://arxiv.org/abs/2410.19057

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