Local well-posedness and time regularity for a fifth-order shallow water equations in analytic Gevrey-Bourgain spaces (Q2204721)

In this paper, the authors are interested in the Cauchy problems for the fifth-order shallow water equations with nonlinear terms, which allow to describe in various cases the flow below a pressure surface in a fluid. With some initial data in analytic Gevrey spaces on the line, they prove that these problems are well-defined. They also study the regularity in the time \(t\) near zero for every \(x\) on the line, improving thus the results of \textit{Y. Jia} and \textit{Z. Huo} [J. Differ. Equations 246, No. 6, 2448--2467 (2009; Zbl 1172.35061)].