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arXiv · 2511.18819

Local-in-time existence of strong solutions to a class of compressible Power-Law flows

Fang Li·Chang Mengge·Guo Zhenhua
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Abstract

We consider a model of the compressible non-Newtonian fluids for power-law flow fulfilling a periodic domain in ${\mathbb R}^3,$ in which the extra stress tensor is induced by a potential with $p(t,x)$-structure. The local-in-time existence of strong solution is proved for all $\frac{7}{5} < \inf p(t,x) \leqslant \sup p(t,x) \leqslant 2.$ Further, an improved blow-up criterion for strong solutions is given in terms of the $L^\infty(0,T;L^3(\Omega))$-norm of the gradient of the velocity.

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Fang Li, Chang Mengge, Guo Zhenhua. 2025-11-24. Local-in-time existence of strong solutions to a class of compressible Power-Law flows. https://arxiv.org/abs/2511.18819

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