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Global Weak Solutions of the Navier-Stokes System with Nonzero Boundary Conditions

2010
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Funkcialaj Ekvacioj
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Consider the Navier-Stokes equations in a smooth bounded domain Ω ⊂ R 3 and a time interval [0, T ), 0 < T ≤ ∞. It is well-known that there exists at least one global weak solution u with vanishing boundary values u ∂Ω = 0 for any given initial value u 0 ∈ L 2 σ (Ω), external force f = div F , F ∈ L 2 0, T ; L 2 (Ω) , and satisfying the strong energy inequality. In this paper we extend this existence result to the case of inhomogeneous boundary values u ∂Ω = g = 0. Given f as above and u 0 ∈ L

doi:10.1619/fesi.53.231
fatcat:h2jkiqzn3rbqdjpzdrteej6pk4