On the well-posedness of the incompressible porous media equation in Triebel-Lizorkin spaces

Boundary value problems

Wenxin Yu¹  Yigang He² 

[1] College of Electrical and Information Engineering, Hunan University, Changsha, P.R. China;School of Electrical and Automation Engineering, Hefei University of Technology, Hefei, P.R. China

关键词: well-posedness;    incompressible porous media equation;    blow-up criterion;    Fourier localization;    Bony’s paraproduct decomposition;    Triebel-Lizorkin space;   

DOI  :  10.1186/1687-2770-2014-95

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we prove the local well-posedness for the incompressible porous media equation in Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. The main tools we use are the Fourier localization technique and Bony’s paraproduct decomposition. MSC:76S05, 76D03.

【 授权许可】

CC BY