$C^{\gamma}$ well-posedness of some non-linear transport equations

J. C. Cantero

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arXiv · 2103.06755

$C^{\gamma}$ well-posedness of some non-linear transport equations

J. C. Cantero

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Abstract

Given $k:\mathbb{R}^n\setminus\{0\} \to \mathbb{R}^n$ a kernel of class $C^2$ and homogeneous of degree $1-n$, we prove existence and uniqueness of H\"older regular solutions for some non-linear transport equations with velocity fields given by convolution of the density with $k$. The Aggregation, the 3D quasi geostrophic, and the 2D Euler equations can be recovered for particular choices of $k$.

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J. C. Cantero. 2021-03-11. $C^{\gamma}$ well-posedness of some non-linear transport equations. https://arxiv.org/abs/2103.06755

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