Geodesic
Regularity bounds on Zakharov system evolutions
Electronic journal of differential equations, Tome 2002 (2002)
Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution $u(t)$ is shown to satisfy an estimate $\|u(t)\|_{H^s} \leq C |t|^{(s-1)+}$, where $H^s$ is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrodinger equation which reduces matters to bilinear estimates.
Classification : 35Q55
Keywords: initial value problems, bilinear estimates, zakharov system, weak turbulence 
@article{EJDE_2002__2002__a118,
     author = {Colliander,  James and Staffilani,  Gigliola},
     title = {Regularity bounds on {Zakharov} system evolutions},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1027.35122},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a118/}
}
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Colliander,  James; Staffilani,  Gigliola. Regularity bounds on Zakharov system evolutions. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a118/