On the generalized porous medium equation in Fourier-Besov spaces

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....

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Hauptverfasser:	Xiao, Weiliang, Zhou, Xuhuan
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Sprache:	eng
Schlagworte:	Mathematics - Analysis of PDEs
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creator	Xiao, Weiliang Zhou, Xuhuan
description	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.
doi_str_mv	10.48550/arxiv.1612.03304
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title	On the generalized porous medium equation in Fourier-Besov spaces
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