Existence and equicontinuity of solutions to the Kirchhoff--Pohozaev wave equation

Abstract

It was recently discovered by Boiti--Manfrin that a variant of the Kirchhoff wave equation introduced by Pohozaev admits infinitely many conserved quantities. In this paper, we obtain explicit formulae for such conserved quantities, as well as introduce a generating function for them that is coercive. These tools are then employed to establish a priori bounds, the propagation of equicontinuity, global well-posedness in ${\mathcal{H}}^s$ for $s\ge \frac{3}{2}$, and the existence of global $C_t{\mathcal{H}}^1$ solutions.