Abstract
A nonlinear partial differential equation, which includes the Novikov equation as a special case, is investigated. The well-posedness of local strong solutions for the equation in the Sobolev space H s (R )w iths > 3 is established. Although the H 1 -norm of the solutions to the nonlinear model does not remain constant, the existence of its local weak solutions in the lower order Sobolev space H s (R )w ith 1≤ s ≤ 3 is established under the assumptions u0 ∈ H s andu0xL∞ < ∞. MSC: 35Q35; 35Q51
Highlights
Novikov [ ] derived the integrable equation with cubic nonlinearities ut – utxx + u ux = uuxuxx + u uxxx, ( )which has been investigated by many scholars
Which has been investigated by many scholars
A Galerkin-type approximation method was used in Himonas and Holliman’s paper [ ] to establish the well-posedness of Eq ( ) in the
Summary
Mi and Mu [ ] obtained many dynamic results for a modified Novikov equation with a peak solution. Proved the local well-posedness for the periodic Cauchy problem of the Novikov equation in Sobolev space with s
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