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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.

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