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Euler equation and holomorphies at low spatial regularity. (Équation d’Euler et holomorphies à faible régularité spatiale.) (French. Abridged English version) Zbl 0834.34077
Summary: We consider the incompressible Euler equation. If the initial speed \(u_0\) is of finite regularity in \(x\) (\(C^{1+ s}\), at least) then all the Lagrangian variables are holomorphic in time and their dependence in \(u_0\) defines \(C^\infty\) operators which are sum of their Taylor’s series. We present next, particular solutions, global in time, for this equation.

34G20 Nonlinear differential equations in abstract spaces
35Q35 PDEs in connection with fluid mechanics
76B99 Incompressible inviscid fluids