Abstract
The existence of local weak solutions for a generalized Novikov equation is established in the Sobolev space with . The pseudo-parabolic regularization technique and several estimates derived from the equation itself are used to prove the existence. MSC:35Q35, 35Q51.
Highlights
Many scholars have paid attention to the study of the integrable Novikov equation [ ]vt – vtxx + v vx = vvxvxx + v vxxx, ( )which has a matrix Lax pair [, ] and is shown to be related to a negative flow in the Sawada-Kotera hierarchy
Himonas and Holliman [ ] applied the Galerkin-type approximation method to prove the well-posedness of strong solutions for Eq ( ) in the Sobolev space
We study the following generalized dissipative Novikov equation: vt – vtxx + v vx = vvxvxx + v vxxx – αv n+ + β∂x v xN, ( )
Summary
[ ] to show the existence and uniqueness of local strong solutions in the Sobolev space with s The local well-posedness for the periodic Cauchy problem of the Novikov equation in the Sobolev space with s is done in We study the following generalized dissipative Novikov equation: vt – vtxx + v vx = vvxvxx + v vxxx – αv n+ + β∂x v xN– , ( )
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