In this paper we study the Cauchy problem for the 4-th order nonlinear equation ${{\partial }_{t}}h+\partial _{x}^{4}h+\partial _{x}^{2}\left( {{\left| {{\partial }_{x}}h \right|}^{\alpha }} \right)=0$ in one dimension for the initial data ${{h}_{0}}$ where $\alpha \ge 5$ and $\alpha \in \mathbb{R}$. Making use of some subtle estimates of the corresponding linear equation and the nonlinear term, Littlewood-Paley theory, two-norm method and contraction mapping principle, we get the local well-posedness result in nonhomogeneous Besov spaces.
WANG Qingkai
,
WU Gang
. Local existence and uniqueness in Besov spaces for the solution of a surface growth model with fractional power nonlinear term[J]. Journal of University of Chinese Academy of Sciences, 0
: 7
-7
.
DOI: 10.7523/j.ucas.2024.052
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