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Existence result for heat-conducting viscous incompressible fluids with vacuum

김현석|조용근
대한수학회 (The Korean Mathematical Society)|2008.05|대한수학회지 (Journal of the KMS)|제45권 제3호|pp. 645-681

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키워드

strong solutionsvacuum.
주제분류수학

초록

The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain Ω ⊂ R³. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of ­ or decay at infinity when ­Ω is unbounded.

Abstract

The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain Ω ⊂ R³. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of ­ or decay at infinity when ­Ω is unbounded.

참고문헌 (27)

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