Andrew Lawrie

Scattering for the radial 3D cubic wave equation

Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in

A Refined Threshold Theorem for (1 + 2)-Dimensional Wave Maps into Surfaces

\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}

Stability of stationary equivariant wave maps from the hyperbolic plane

and subcritical with respect to the conserved energy. Here we prove that if the critical norm of a solution remains bounded on the maximal time-interval of existence, then the solution must in fact be global-in-time and scatter to free waves as

Two-bubble dynamics for threshold solutions to the wave maps equation

t \to \pm \infty

Characterization of large energy solutions of the equivariant wave map problem: II

.

Relaxation of Wave Maps Exterior to a Ball to Harmonic Maps for All Data

The recently established threshold theorem for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scatter on

Channels of energy for the linear radial wave equation

{\mathbb{R}^{1+2}}

Scattering for wave maps exterior to a ball

R1+2. In this note we give a refinement of this theorem when the target is a closed orientable surface, by taking into account an additional invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact twice the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state. We also give a discussion on the formulation of a refined threshold conjecture for the energy critical SU(2) Yang–Mills equation on