Global results for a Cauchy problem related to biharmonic wave maps

Abstract

We prove global existence of a derivative bi-harmonic wave equation with a non-generic quadratic nonlinearity and small initial data in the scaling critical space ${\dot{B}}_{\frac{d}{2}}^{2,1}({\mathbb{R}}^d)\times {\dot{B}}_{\frac{d}{2}-2}^{2,1}({\mathbb{R}}^d)$ for $d\ge 3$. Since the solution persists higher regularity of the initial data, we obtain a small data global regularity result for the biharmonic wave maps equation for a certain class of target manifolds including the sphere.

References in corpus (4)

• On the Division Problem for the Wave Maps Equation
• Biharmonic wave maps into spheres
• Biharmonic wave maps: Local wellposedness in high regularity
• Energy bounds for a fourth-order equation in low dimensions related to wave maps