In this Note, we consider problems of endpoint Strichartz estimates for the kinetic equation in one dimension. The fundamental result obtained in Theorem 1 is proved using two different methods: in the first we construct an explicit counterexample; in the second uses a duality argument.
Dans cette Note on étudie des problèmes d'estimations de Strichartz dans un cas limite pour l'équation cinétique. Dans le cas de la dimension un, le résultat fondamental du Théorème 1 est démontré par deux méthodes : dans la première on construit un contrexemple explicite, dans le seconde on utilise un argument de dualité.
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@article{CRMATH_2007__345_5_253_0, author = {Guo, Zihua and Peng, Lizhong}, title = {Endpoint {Strichartz} estimate for the kinetic transport equation in one dimension}, journal = {Comptes Rendus. Math\'ematique}, pages = {253--256}, publisher = {Elsevier}, volume = {345}, number = {5}, year = {2007}, doi = {10.1016/j.crma.2007.07.002}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.07.002/} }
TY - JOUR AU - Guo, Zihua AU - Peng, Lizhong TI - Endpoint Strichartz estimate for the kinetic transport equation in one dimension JO - Comptes Rendus. Mathématique PY - 2007 SP - 253 EP - 256 VL - 345 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.07.002/ DO - 10.1016/j.crma.2007.07.002 LA - en ID - CRMATH_2007__345_5_253_0 ER -
%0 Journal Article %A Guo, Zihua %A Peng, Lizhong %T Endpoint Strichartz estimate for the kinetic transport equation in one dimension %J Comptes Rendus. Mathématique %D 2007 %P 253-256 %V 345 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.07.002/ %R 10.1016/j.crma.2007.07.002 %G en %F CRMATH_2007__345_5_253_0
Guo, Zihua; Peng, Lizhong. Endpoint Strichartz estimate for the kinetic transport equation in one dimension. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 253-256. doi : 10.1016/j.crma.2007.07.002. http://archive.numdam.org/articles/10.1016/j.crma.2007.07.002/
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⁎ Research supported by NNSF of China No.10471002, RFDP of China No: 20060001010.