The Cauchy Problem of the Modified Kawahara Equation (Journal of Partial Differential Equations, 2006)
In this paper, we consider the local and global solutions for the modified Kawahara equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from Kato's smoothing effect and the maximal function (in time) estimate for the free Kawahara operator e^{-ϒ^{t∂^5_x}}.
Keywords: Modified Kawahara equation; Cauchy problem; Littlewood-Paley decomposition; Besov space