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| WELL-POSEDNESS FOR THE CAUCHY PROBLEMTO THE HIROTA EQUATION IN SOBOLEVSPACES OF NEGATIVE INDICES |
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Citation： |
HUO Zhaohui,JIA Yueling.WELL-POSEDNESS FOR THE CAUCHY PROBLEMTO THE HIROTA EQUATION IN SOBOLEVSPACES OF NEGATIVE INDICES[J].Chinese Annals of Mathematics B,2005,26(1):75~88 |
| Page view： 1290
Net amount： 754 |
Authors： |
HUO Zhaohui; JIA Yueling |
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| Abstract： |
The local well-posedness of the Cauchy problem for the Hirota
equation is established for low regularity data in Sobolev spaces
$H^s(s\geq -\frac{1}{4}).$ Moreover, the global well-posedness for
$L^2$ data follows from the local well-posedness and the conserved
quantity. For data in $H^s(s>0)$, the global well-posedness is
also proved. The main idea is to use the generalized trilinear
estimates, associated with the Fourier restriction norm method. |
Keywords： |
Fourier restriction norm, Trilinear estimates, Hirota equation, Low regularity,
Global well-posedness |
Classification： |
35Q53, 35Q55, 35E15 |
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