Problem on the motion of two compressible fluids separated by a closed free interface. (English. Russian original) Zbl 0911.76079

J. Math. Sci., New York 99, No. 1, 837-853 (2000); translation from Zap. Nauchn. Semin. POMI 243, 61-86 (1997).
We consider the evolution of two barotropic capillary viscous compressible fluids occuping the whole space \(\mathbb{R}^3\) and separated by a closed free interface. Under some restrictions on the fluid viscosities, we obtain the local (in time) unique solvability of this problem in Sobolev-Slobodetskij spaces. The proof is based on the method of successive approximations and on an explicit solution of a model linear problem with the plane interface between the fluids.


76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
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