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

Wenxin Yu1* and Yigang He2

Author Affiliations

1 College of Electrical and Information Engineering, Hunan University, Changsha, 410000, P.R. China

2 School of Electrical and Automation Engineering, Hefei University of Technology, Anhui Pro., Hefei, 230009, P.R. China

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Boundary Value Problems 2014, 2014:95  doi:10.1186/1687-2770-2014-95

Published: 6 May 2014

Abstract

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.

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