Perfect incompressible fluids / Jean-Yves Chemin

Auteur principal : Chemin, Jean-Yves, 1959-, AuteurType de document : MonographieCollection : Oxford lecture series in mathematics and its applications, 14Langue : anglais.Pays: Etats Unis.Éditeur : New York : Oxford University Press, 1998Description : 1 vol. (X-187 p.) ; 24 cmISBN: 0198503970.Bibliographie : Bibliogr. p. [181]-185. Index.Sujet MSC : 76-02, Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Bxx, Fluid mechanics - Incompressible inviscid fluids
35Q35, PDEs of mathematical physics and other areas of application, PDEs in connection with fluid mechanics
76X05, Fluid mechanics, Ionized gas flow in electromagnetic fields; plasmic flow
Item type: Monographie
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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

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