Solvability in weighted Hölder spaces for a problem governing the evolution of two compressible fluids. (English. Russian original) Zbl 1082.35118

J. Math. Sci., New York 127, No. 2, 1849-1868 (2005); translation from Zap. Nauchn. Semin. POMI 295, 57-89 (2003).
The authors study the motion of two compressible barotropic fluids separated by a closed surface. Surface tensions on the interface are taken into account. The immiscible fluids have different dynamical viscosities. The problem is to find the boundary between the fluids, their densities, and their velocities from the boundary-value problem for the Navier-Stokes system. The condition of no mass transfer through the boundary between the flows is added to the system. The authors prove the existence and uniqueness of the solution to this problem in Hölder spaces with power-like weight in infinity (with respect to spatial variables). Fixed point theorems and functional estimations are used as a tool.


35Q30 Navier-Stokes equations
35R35 Free boundary problems for PDEs
35A15 Variational methods applied to PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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