Regularity Bounds on Zakharov System Evolutions
Southwest Texas State University, Department of Mathematics
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.
Initial value problems, Bilinear estimates, Zakharov system, Weak turbulence
Colliander, J., & Staffilani, G. (2002). Regularity bounds on Zakharov system evolutions. <i>Electronic Journal of Differential Equations, 2002</i>(75), pp. 1-11.