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On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid. (English) Zbl 0874.35097

The authors consider the global solution of the Navier-Stokes equations describing the compressible heat-conducting fluid in a bounded domain \(\Omega_t \subset \mathbb{R}^3\), which depends on time \(t\). The free boundary \(\partial\Omega_t\) is governed by the surface tension and constant exterior pressure. Using some differential inequalities, the authors prove the existence of a global in time solution near a constant stationary state (the constant stationary state means that \(\Omega_t\) is a fixed ball, the density and temperature are constant, the initial velocity, external forces, and heat fluxes vanish).
Reviewer: O.Titow (Berlin)

MSC:

35Q35 PDEs in connection with fluid mechanics
35R35 Free boundary problems for PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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