Gevrey regularizing effect for the initial value problem for a dispersive operator
The Gevrey regularizing effect for equations of Schrödinger type has been studied by other authors. It is known that the initial value problem \[ \begin{cases} i\partial_tu+ \Delta^lu &= f(u),\\ u(0,x) &= u_0(x)\end{cases} \] has a solution \(u(t, x)\) which belongs to a Gevrey class of order \(\max(s/2l, 1)\) in \(t\neq 0\) if the initial data \(u_0(x)\) belongs to a Gevrey class of order \(s\). In this paper, the author studies the Gevrey regularizing effect of this initial value problem where \(\Delta^l\) is replaced by a semi-elliptic operator \(A\).
scientific article; zbMATH DE number 2147092