TY - JOUR
T1 - The Cauchy Problem of the Modified Kawahara Equation
AU - Guixiang Xu 
JO - Journal of Partial Differential Equations
VL - 2
SP - 126
EP - 146
PY - 2006
DA - 2006/05
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5324.html
KW - Modified Kawahara equation
KW - Cauchy problem
KW - Littlewood-Paley decomposition
KW - Besov space
AB - <p>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&#39;s smoothing effect and the maximal function (in time) estimate for the free Kawahara operator e^{-ϒ^{t∂^5_x}}.</p>