On the well-posedness of the incompressible porous media equation in Triebel-Lizorkin spaces
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
Boundary Value Problems 2014, 2014:95 doi:10.1186/1687-2770-2014-95Published: 6 May 2014
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.