Large-time behavior of the weak solution to 3D Navier-Stokes equations

2012/09/09 by Ramm, A. G.
#35-XX #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1209.1825

Abstract

The weak solution to the Navier-Stokes equations in a bounded domain D ⊂ ℝ³ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t ≥ 0. In a bounded domain D the solution decays exponentially fast as t→ ∞ if the force term decays at a suitable rate.

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