Publication

GLOBAL RESULTS FOR A CAUCHY PROBLEM RELATED TO BIHARMONIC WAVE MAPS

Tobias Johannes Schmid
2024

Abstract

We prove global existence of a derivative biharmonic wave equation with a nongeneric quadratic non-linearity and small initial data in the scaling critical space Ḃ2,1 d/2(ℝd) × Ḃ2,1 d/2−2(ℝd) for d ≥ 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.

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