Global solutions and stability properties of the 5th order Gardner equation

Abstract

In this work, we deal with the initial value problem of the 5th-order Gardner equation in $\mathbb{R}$, presenting the local well-posedness result in $H^2(\mathbb{R})$. As a consequence of the local result, in addition to $H^2$-energy conservation law, we are able to prove the global well-posedness result in $H^2(\mathbb{R})$. Finally, we present a stability result for 5th order Gardner breather solution in the Sobolev space $H^2(\mathbb{R})$.

34 pages, typos corrected, references updated, title of the latter version changed

References in corpus (3)

• Low regularity solutions of two fifth-order KdV type equations
• Nonlinear wave interactions for the Benjamin-Ono equation
• Parabolic smoothing effect and local well-posedness of fifth order semilinear dispersive equations on the torus