Pour l'équation KZK dans la classe des fonctions périodiques en x et de moyennes nulles, on a étudié la dérivation à partir du système de Navier–Stokes isentropique et la validation de son approximation, l'existence, l'unicité et la stabilité de la solution. On a prouvé que la solution est globale en temps pour des données initiales suffisement petites avec et que la solution présente une onde de choc si .
For the KZK equation in the class of x-periodic and of zero mean value functions we have analysed the following: the derivation from Navier–Stokes system and the validity of its approximation, the existence, uniqueness and stability of the solution. The solution is proved to be global in time for sufficient small initial data with and to have a blow-up if .
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@article{CRMATH_2007__344_5_337_0, author = {Rozanova, Anna}, title = {The {Khokhlov{\textendash}Zabolotskaya{\textendash}Kuznetsov} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {337--342}, publisher = {Elsevier}, volume = {344}, number = {5}, year = {2007}, doi = {10.1016/j.crma.2007.01.010}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.010/} }
TY - JOUR AU - Rozanova, Anna TI - The Khokhlov–Zabolotskaya–Kuznetsov equation JO - Comptes Rendus. Mathématique PY - 2007 SP - 337 EP - 342 VL - 344 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.01.010/ DO - 10.1016/j.crma.2007.01.010 LA - en ID - CRMATH_2007__344_5_337_0 ER -
Rozanova, Anna. The Khokhlov–Zabolotskaya–Kuznetsov equation. Comptes Rendus. Mathématique, Tome 344 (2007) no. 5, pp. 337-342. doi : 10.1016/j.crma.2007.01.010. http://www.numdam.org/articles/10.1016/j.crma.2007.01.010/
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