Daniel Tataru

Near Soliton Evolution for 2-Equivariant Schrödinger Maps in Two Space Dimensions

We consider equivariant solutions for the Schrödinger Map equation in 2 + 1 2+1 dimensions, with values into S 2 \mathbb {S}^2 . Within each equivariance class m ∈ Z m \in \mathbb {Z} this admits a lowest energy nontrivial steady state Q m Q^m , which extends to a two dimensional...

Nonlinear interpolation and the flow map of quasilinear equations

We prove an interpolation theorem for nonlinear functionals defined on scales of Banach spaces that generalize Besov spaces. It applies to functionals defined only locally, requiring only some weak Lipschitz conditions, extending those introduced by Lions and Peetre. Our analysis...

Enhanced Lifespan Bounds for 1D Quasilinear Klein–Gordon Flows

Abstract In this article we consider one-dimensional scalar quasilinear Klein–Gordon equations with general nonlinearities, on both $${\mathbb {R}}$$ R and $${\mathbb {T}}$$ T . By employing a refined modified-energy framework of Ifrim and Tataru, we investigate long time lifespa...