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arXiv · 2407.18425

Fujita phenomena in nonlinear fractional Rayleigh-Stokes equations

Yiming Jiang·Jingchuang Ren·Yawei Wei
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Abstract

This paper concerns the Cauchy problems for the nonlinear Rayleigh-Stokes equation and the corresponding system with time-fractional derivative of order $\alpha\in(0,1)$, which can be used to simulate the anomalous diffusion in viscoelastic fluids. It is shown that there exists the critical Fujita exponent which separates systematic blow-up of the solutions from possible global existence, and the critical exponent is independent of the parameter $\alpha$. Different from the general scaling argument for parabolic problems, the main ingredients of our proof are suitable decay estimates of the solution operator and the construction of the test function.

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Yiming Jiang, Jingchuang Ren, Yawei Wei. 2024-07-25. Fujita phenomena in nonlinear fractional Rayleigh-Stokes equations. https://arxiv.org/abs/2407.18425

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