Regularity Bounds on Zakharov System Evolutions
Date
2002-08-20
Authors
Colliander, James
Staffilani, Gigliola
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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)||Hs ≤ C|t|(s - 1)+, where Hs is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrödinger equation which reduces matters to bilinear estimates.
Description
Keywords
Initial value problems, Bilinear estimates, Zakharov system, Weak turbulence
Citation
Colliander, J., & Staffilani, G. (2002). Regularity bounds on Zakharov system evolutions. <i>Electronic Journal of Differential Equations, 2002</i>(75), pp. 1-11.