Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations

2000/07/05 by Steve Shkoller, Shkoller, Steve
Mathematics · #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q35

paper · pdf · doi:10.48550/arxiv.math/0007027

arxiv created 2000/07/05 · arxiv updated 2009/11/30

Abstract

We present a very simple proof of the global existence of a C^∞ Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with boundary) which has C^∞ dependence on initial data u₀ in the class of H^s divergence-free vector fields for s>2.

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