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arXiv · 2509.01067

The Euler equations with variable coefficients

Benjamin Ingimarson·Igor Kukavica·Amjad Tuffaha
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Abstract

We establish local-in-time existence for the Euler equations on a bounded domain with space-time dependent variable coefficients, given initial data $v_0 \in H^r$ under the optimal regularity condition $r > 2.5$. In the case $r = 3$, we further prove a Beale-Kato-Majda criterion that relates blow-up in the $H^r$ norm to the BMO norm of the variable vorticity $\zeta$.

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Benjamin Ingimarson, Igor Kukavica, Amjad Tuffaha. 2025-09-01. The Euler equations with variable coefficients. https://arxiv.org/abs/2509.01067

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