On the Generalized Porous Medium Equation in Fourier-Besov Spaces

On the Generalized Porous Medium Equation in Fourier-Besov Spaces

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.

Author Details

Weiliang Xiao

Xuhuan Zhou