Global well-posedness of the 3D incompressible porous media equation with critical dissipation in Triebel-Lizorkin spaces

In this paper, we study the global well-posedness of the 3D incompressible critical dissipative porous media equation with small initial data in the Triebel-Lizorkin space F p , q s ( R 3 ) . By a pointwise exponential decay estimate on the Poisson semigroup e − t ν − Δ and the Fourier localization technique, we generalize the global well-posedness in the Sobolev spaces H p s ( R 3 ) = F p , 2 s ( R 3 ) and H s ( R 3 ) = F 2 , 2 s ( R 3 ) into the general Triebel-Lizorkin spaces F p , q s ( R 3 ) with s > 3 p , p , q ∈ ( 1 , ∞ ) .