Year: 2020
Author: Weiliang Xiao, Xuhuan Zhou
Journal of Mathematical Study, Vol. 53 (2020), Iss. 3 : pp. 316–328
Abstract
We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n3.20.05
Journal of Mathematical Study, Vol. 53 (2020), Iss. 3 : pp. 316–328
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Porous medium equation well-posedness blowup criterion Fourier-Besov spaces.