Abstract
The well-posedness of Cauchy problem for the Hirota equation is obtained in Sobolev spaces H s . Local result is established for initial data in H s ( s ⩾ 1 4 ) by using the Fourier restriction norm method. Moreover, the local solution is global for the initial data in H s ( s ⩾ 1 ) by the generalized trilinear estimates associated with the Fourier restriction norm method.
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