CLASSICAL SOLVABILITY OF THE TWO-PHASE STEFAN PROBLEM IN A VISCOUS INCOMPRESSIBLE FLUID FLOW

DOI10.1142/S0218202502001696zbMath1040.35151MaRDI QIDQ4798967

Atusi Tani, Yoshiaki Kusaka

Publication date: 16 March 2003

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenessNavier-Stokes equationclassical solutionenergy dissipationfree boundary problemsStefan problemsthermal balance equation

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stefan problems, phase changes, etc. (80A22) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35)

Related Items (6)

Qualitative Behaviour of Incompressible Two-Phase Flows with Phase Transitions: The Case of Non-Equal Densities ⋮ Global-in-time strong solvability of the multi-dimensional one-phase Stefan problem for an incompressible viscous fluid ⋮ On well-posedness of incompressible two-phase flows with phase transitions: the case of non-equal densities ⋮ Nonlinear convection-dispersion models with a distributed pollutant source. I: Direct initial boundary value problems ⋮ Mathematical models and methods in the water industry ⋮ On Fourier multipliers in function spaces with partial Hölder condition and their application to the linearized Cahn-Hilliard equation with dynamic boundary conditions

Cites Work

• Solvability of a noncoercive initial-boundary value problem for a Stokes system in Hölder classes of functions (half-space case)
• Classical solutions of the Stefan problem
• Local existence and uniqueness of solutions of the Stefan problem with surface tension and kinetic undercooling
• On the Classical Solvability of the Stefan Problem in a Viscous Incompressible Fluid Flow

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