Regularity bounds on Zakharov system evolutions
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 ear...
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| Published in: | Electronic journal of differential equations Vol. 2002; no. 75; pp. 1 - 11 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Texas State University
01-08-2002
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| 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 $|u(t)|_{H^s} leq C |t|^{(s-1)+}$, 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. |
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| AbstractList | 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. |
| Author | Gigliola Staffilani James Colliander |
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| Snippet | Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution $u(t)$ is shown... |
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| SubjectTerms | bilinear estimates initial value problems weak turbulence Zakharov system |
| Title | Regularity bounds on Zakharov system evolutions |
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