Global classical solution of Muskat free boundary problem

[摘要] In this paper the Muskat problem which describes a two-phase flow of two fluids, for example, oil and water, in porous media is discussed. The problem involves in seeking two time-dependent harmonic functions u(1)(x, y, t) and u(2)(x, y, t) in oil and water regions, respectively, and the interface between oil and water, i.e., the free boundary Gamma: y = rho(x, t), such that on the free boundary u(1) = u(2), V-n = -k(1) partial derivativeu(1)/partial derivativen = -k(2) partial derivativeu(2)/partial derivativen, where n the unit normal vector on the free boundary toward oil region, V-n is the normal velocity of the free boundary Gamma, k(1) and k(2) are positive constants satisfying k(1) > k(2). We prove the existence of classical solution globally in time under some reasonable assumptions. The argument developed in this paper can be used in any multidimensional case. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-12-15

[关键词] global existence;free boundary;Muskat problem