13 papers
Bubble decomposition for the harmonic map heat flow in the equivariant case
Jacek Jendrej, Andrew Lawrie
We consider the harmonic map heat flow for maps from the plane taking values in the sphere, under equivariant symmetry. It is known that solutions to the initial value problem can…
Soliton resolution for the energy-critical nonlinear wave equation in the radial case
Jacek Jendrej, Andrew Lawrie
We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions . This equation has a unique (up to sign and scale…
Continuous time soliton resolution for two-bubble equivariant wave maps
Jacek Jendrej, Andrew Lawrie
We consider the energy-critical wave maps equation from 1+2 dimensional Minkowski space into the 2-sphere, in the equivariant case. We prove that if a wave map decomposes, along a…
Uniqueness of two-bubble wave maps
Jacek Jendrej, Andrew Lawrie
This is the second part of a two-paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider…
The Lie Detector
Arthur Young, Andrew Lawrie
How many free variables do we really need to build a credible model of a physical system? Currently there is no systematic approach; we appeal to some physical principles, tune fre…
Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line
Jacek Jendrej, Michał Kowalczyk, Andrew Lawrie
This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such a model admits static solutions called kinks and ant…