Abstract
AbstractThis 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 in 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 space with is small.
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Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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