Premium
Global well‐posedness for incompressible flow in porous media with partial diffusion or fractional diffusion
Author(s) -
Guo Yana,
Shang Haifeng
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700129
Subject(s) - diffusion equation , porous medium , supercritical fluid , diffusion , compressibility , mathematics , geodetic datum , norm (philosophy) , mathematical analysis , heat equation , anomalous diffusion , partial differential equation , physics , porosity , mechanics , thermodynamics , materials science , innovation diffusion , geology , computer science , economics , knowledge management , economy , geodesy , political science , law , composite material , service (business)
This paper examines the equation of heat transfer with fractional diffusion or partial diffusion of an incompressible fluid in a porous medium. We establish two main results. The first result is the global regularity for the equation with partial diffusion when the norm of initial datum inH 1 ( R 3 )is small. The second result is to show that for the supercritical case, the equation with fractional diffusion has a unique global solution provided that the norm of initial datum in the Besov spaceB ̇ p , ∞ s ( R 3 )with s ≥ 1 − α + 3 pis small.