Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations
This paper considers the Cauchy problem for \[ (1-\partial_x^2)(u_t+f(u)_x)+\partial_x[g(u)+\frac{1}{2} f''(u)u_x^2]=0, \] where $x\in\mathbb{R}$, the initial condition is in $H^s(\mathbb{R})$ with $s>3/2$, $f$ and $g$ are smooth, $f''\geq \gamma$ for some positive constant $\gamma$, and $g$ is bounded above or bounded below. The main result is an improvement of a local blow-up criterion given by \textit{L. Brandolese} and \textit{M. F. Cortez} [J. Differ. Equations 256, No. 12, 3981--3998 (2014; Zbl 1293.35053); J. Funct. Anal. 266, No. 12, 6954--6987 (2014; Zbl 1295.35009)], along similar lines.
scientific article; zbMATH DE number 6946028
scientific article