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arXiv · 2510.17350

Sobolev instability for perturbations of periodic transport equations

Gabriel Rivière·Maria Teresa Rotolo
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Abstract

We consider linear and time-dependent perturbations of periodic transport equations on the two-dimensional torus. For generic perturbations, we prove the existence of a large class of initial data whose Sobolev norms diverge exponentially fast. In higher dimensions, this remains true under a Morse-Smale assumption on the resonant part of the perturbation. In both cases, this is achieved by a normal form procedure and by studying Sobolev instabilities for time-dependent perturbations of Morse-Smale transport equations. The latter are analyzed on general compact manifolds using techniques from microlocal analysis and hyperbolic dynamics.

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Gabriel Rivière, Maria Teresa Rotolo. 2025-10-20. Sobolev instability for perturbations of periodic transport equations. https://arxiv.org/abs/2510.17350

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