Colliander, JamesStaffilani, Gigliola2020-08-172020-08-172002-08-20Colliander, J., & Staffilani, G. (2002). Regularity bounds on Zakharov system evolutions. <i>Electronic Journal of Differential Equations, 2002</i>(75), pp. 1-11.1072-6691https://hdl.handle.net/10877/12408Spatial 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 estimateu(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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalInitial value problemsBilinear estimatesZakharov systemWeak turbulenceArticle