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

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

2000-07-05

arxiv.org/abs/math/0007027v1

Mathematics

Analysis of PDEs

Scientific paper

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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