Geodesic
Cauchy problem for dispersive equations in \(\alpha\)-modulation spaces
Electronic journal of differential equations, Tome 2014 (2014)
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},
     year = {2014},
     volume = {2014},
     zbl = {1297.35083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a75/}
}
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AU  - Chen,  Jiecheng
TI  - Cauchy problem for dispersive equations in \(\alpha\)-modulation spaces
JO  - Electronic journal of differential equations
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%A Chen,  Jiecheng
%T Cauchy problem for dispersive equations in \(\alpha\)-modulation spaces
%J Electronic journal of differential equations
%D 2014
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%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a75/
%G en
%F EJDE_2014__2014__a75
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/