Existence of global weak solutions to a parabolic $p$-Laplacian problem with convective term

Angelica Pia Di Feola; Michael Ruzicka

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arXiv · 2510.05847

Existence of global weak solutions to a parabolic $p$-Laplacian problem with convective term

Angelica Pia Di Feola·Michael Ruzicka

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Abstract

For a given bounded domain $\Omega \subset \mathbb R^3$, with $C^2$ boundary, and a given instant of time $T>0$, we prove the existence of a global weak solution on $(0,T)$, which satisfies a maximum principle, to a parabolic $p$-Laplacian system with convective term without divergence constraint for any $p\in (1,2)$.

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Angelica Pia Di Feola, Michael Ruzicka. 2025-10-07. Existence of global weak solutions to a parabolic $p$-Laplacian problem with convective term. https://arxiv.org/abs/2510.05847

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