Nondecreasing analytic radius for the a Kawahara-Korteweg-de-Vries equation

Abstract

By using linear, bilinear, and trilinear estimates in Bourgain-type spaces and analytic spaces, the local well-posedness of the Cauchy problem for the a Kawahara-Korteweg-de-Vries equation$ \partial_{t}u+\omega\partial_{x}^{5}u+\nu \partial_{x}^{3}u+\mu\partial_{x}u^{2}+\lambda\partial_{x}u^{3}+\mathfrak{d}(x)u = 0, $was established for analytic initial data $ u_{0} $. Besides, based on the obtained local result, together with an analytic approximate conservation law, we prove that the global solutions exist. Furthermore, the analytic radius has a fixed positive lower bound uniformly for all time.

Keywords

• analytic radius
• kawahara-korteweg-de-vries equation
• damped effect
• nonlinear equations