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

Steve Shkoller

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arXiv · math/0007027

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

Steve Shkoller

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Abstract

We present a very simple proof of the global existence of a $C^\infty$ Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with boundary) which has $C^\infty$ dependence on initial data $u_0$ in the class of $H^s$ divergence-free vector fields for $s>2$.

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Steve Shkoller. 2000-07-05. Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations. https://arxiv.org/abs/math/0007027

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