Perfect incompressible fluids / Jean-Yves Chemin

The book presents recent results on the Cauchy problem for the Euler equations of a perfect incompressible fluid. A local uniqueness and existence theorem is proved in a Hölder space C r , r>1, when the initial data are Hölder continuous. In the two-dimensional case this theorem becomes global in the following cases: the case of periodic initial data, the case when the gradient of initial velocity belongs to L p , p>1, and finally, the case when initial velocity is a bounded energy perturbation of a stationary solution. All the other results of the book are also obtained in the two-dimensional case, whose advantage is the conservation of vorticity along the flow of the vector field solution. (Zentralblatt)

Bibliogr. p. [181]-185. Index