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Positivity theorem. (English) Zbl 0854.35084
Summary: We show the positivity of the solution of the continuity equation of the Navier-Stokes system, with boundary conditions considered in [S. N. Antontsev, A. V. Kazhikhov and V. N. Monakhov, Boundary value problems in the mechanics of inhomogeneous fluids. (Russian), Novosibirsk: Nauka (1983; Zbl 0568.76001)]. From this result it follows the uniqueness of the solution. This enables us to simplify the solving of the whole nonlinear Navier-Stokes system in a weak formulation.
MSC:
35Q30 Navier-Stokes equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Citations:
Zbl 0568.76001
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References:
[1] Antoncev S. N., Kazhikhov A. V., Monakhov V. N.: Boundary Value Problems in Nonhomogeneous Fluid Mechanics. (in russian), Nauka, Novosibirsk, 1983.
[2] Fučík S., Kufner A.: Nonlinear Differential Equations. Elsevier Scientifìc Publishing Company, Amsterdam-Oxford-New York, 1980.
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