Comptes Rendus
no. 5
Partial Differential Equations
Endpoint Strichartz estimate for the kinetic transport equation in one dimension
[Estimations de Strichartz dans un cas limite pour l'équation de transport cinétique unidimensionnelle]

Présenté par : Jean-Michel Bony

Zihua Guo1 ; Lizhong Peng1
1 LMAM, School of Mathematical Sciences, Changchun Yuan, Peking University, Beijing 100871, China
Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 253-256.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.002

Zihua Guo 1 ; Lizhong Peng 1

1 LMAM, School of Mathematical Sciences, Changchun Yuan, Peking University, Beijing 100871, China 
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Zihua Guo; Lizhong Peng. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.002/

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  • Shohei Nakamura The orthonormal Strichartz inequality on torus, Transactions of the American Mathematical Society, Volume 373 (2019) no. 2, p. 1455 | DOI:10.1090/tran/7982
  • Neal Bez; Sanghyuk Lee; Shohei Nakamura; Yoshihiro Sawano Sharpness of the Brascamp–Lieb inequality in Lorentz spaces, Electronic Research Announcements in Mathematical Sciences, Volume 24 (2017) no. 0, p. 53 | DOI:10.3934/era.2017.24.006
  • Jonathan Bennett; Neal Bez; Susana Gutiérrez; Sanghyuk Lee On the Strichartz Estimates for the Kinetic Transport Equation, Communications in Partial Differential Equations, Volume 39 (2014) no. 10, p. 1821 | DOI:10.1080/03605302.2013.850880
  • Evgeni Y. Ovcharov Counterexamples to Strichartz estimates for the kinetic transport equation based on Besicovitch sets, Nonlinear Analysis: Theory, Methods Applications, Volume 74 (2011) no. 7, p. 2515 | DOI:10.1016/j.na.2010.12.007
  • Evgeni Y. Ovcharov Strichartz Estimates for the Kinetic Transport Equation, SIAM Journal on Mathematical Analysis, Volume 43 (2011) no. 3, p. 1282 | DOI:10.1137/100803808

Cité par 7 documents. Sources : Crossref

⁎ Research supported by NNSF of China No.10471002, RFDP of China No: 20060001010.

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