Abstract :
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 u1(x,y, t) and u2(x,y, t) in oil and water regions, respectively, and the interface
between oil and water, i.e., the free boundary Γ : y = ρ(x, t), such that on the free boundary
u1 = u2, Vn =−k1
∂u1
∂n =−k2
∂u2
∂n
,
where n the unit normal vector on the free boundary toward oil region, Vn is the normal velocity of
the free boundary Γ , k1 and k2 are positive constants satisfying k1 > k2. 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.
2003 Elsevier Inc. All rights reserved
