In this work, we deal with the initial value problem of the 5th-order Gardner equation in R, presenting the local well-posedness result in H2(R). As a consequence of the local result, in addition to H2-energy conservation law, we are able to prove the global well-posedness result in H2(R). Finally as a direct application, we prove that some globally defined functions, e.g. breather solutions of 5th order Gardner equation, are H2(R) stable.
- Global well-posedness
- Higher order Gardner equation