Geodesic
Cauchy problem for dispersive equations in $\alpha$-modulation spaces
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we consider the Cauchy problem for dispersive equations in $\alpha$-Modulation spaces. For this purpose, we find a method for estimating $u^k$ in alpha-modulation spaces when k is not an integer, and develop a Strichartz estimate in $M_{p,q}^{s,\alpha}$ which is based on semigroup estimates. In the local case, we that the domain of p is independent of $\alpha$, which is also the case in the Modulation spaces and in the Besov space.
Classification : 35A01, 35A02, 35L05
Keywords: alpha-modulation spaces, dispersive equation, Cauchy problem 
@article{EJDE_2014__2014__a75,
     author = {Huang, Qiang and Chen, Jiecheng},
     title = {Cauchy problem for dispersive equations in $\alpha$-modulation spaces},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a75/}
}
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Huang, Qiang; Chen, Jiecheng. Cauchy problem for dispersive equations in $\alpha$-modulation spaces. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a75/