55 citations · 196 across the 26 of their papers we have counts for
33 papers · 1 filter
Classification of kink clusters for scalar fields in dimension 1+1
Jacek Jendrej, Andrew Lawrie
We consider a real scalar field equation in dimension 1+1 with an even, positive self-interaction potential having two non-degenerate zeros (vacua) 1 and -1. Such a model admits no…
Continuous in time bubble decomposition for the harmonic map heat flow
Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag
We consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen seque…
Dynamics of kink clusters for scalar fields in dimension 1+1
Jacek Jendrej, Andrew Lawrie
We consider a real scalar field equation in dimension 1+1 with an even positive self-interaction potential having two non-degenerate zeros (vacua) 1 and -1. It is known that such a…
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…
Soliton resolution for energy-critical wave maps in the equivariant case
Jacek Jendrej, Andrew Lawrie
We consider the equivariant wave maps equation , in all equivariance classes . We prove that every finite energy solution resol…
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…
An asymptotic expansion of two-bubble wave maps
Jacek Jendrej, Andrew Lawrie
This is the first 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 t…
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…
Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane Under the Schrödinger Maps Evolution
Andrew Lawrie, Jonas Lührmann, Sung-Jin Oh +1
We consider the Cauchy problem for the Schrödinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studie…
Dynamics of Bubbling Wave Maps with Prescribed Radiation
Jacek Jendrej, Andrew Lawrie, Casey Rodriguez
We study energy critical one-equivariant wave maps taking values in the two-sphere. It is known that any finite energy wave map that develops a singularity does so by concentrating…
Scattering for defocusing energy subcritical nonlinear wave equations
Benjamin Dodson, Andrew Lawrie, Dana Mendelson +1
We consider the Cauchy problem for the defocusing power type nonlinear wave equation in -dimensions for energy subcritical powers in the range . We prove that…
Local smoothing estimates for Schrödinger equations on hyperbolic space
Andrew Lawrie, Jonas Luhrmann, Sung-Jin Oh +1
We establish global-in-time frequency localized local smoothing estimates for Schrödinger equations on hyperbolic space . In the presence of symmetric first and zerot…
Two-bubble dynamics for threshold solutions to the wave maps equation
Jacek Jendrej, Andrew Lawrie
We consider the energy-critical wave maps equation in the equivariant case, with equivariance degree . It is known that initial data of…
Conditional stable soliton resolution for a semi-linear Skyrme equation
Andrew Lawrie, Casey Rodriguez
We study a semi-linear version of the Skyrme system due to Adkins and Nappi. The objects in this system are maps from -dimensional Minkowski space into the -sphere and 1-…
The Cauchy problem for wave maps on hyperbolic space in dimensions
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
We establish global well-posedness and scattering for wave maps from -dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small i…
Equivariant Wave Maps on the Hyperbolic Plane with Large Energy
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space into surfaces of revolution that was initiated in [13, 14]. When the target is t…
A refined threshold theorem for (1+2)-dimensional wave maps into surfaces
Andrew Lawrie, Sung-Jin Oh
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 har…
Gap Eigenvalues and Asymptotic Dynamics of Geometric Wave Equations on Hyperbolic Space
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
In this paper we study -equivariant wave maps from the hyperbolic plane into the -sphere as well as the energy critical equivariant Yang-Mills problem on -dimensio…
Profile decompositions for wave equations on hyperbolic space with applications
Andrew Lawrie, Sung-Jin Oh, Sohrab Shahshahani
The goal for this paper is twofold. Our first main objective is to develop Bahouri-Gerard type profile decompositions for waves on hyperbolic space. Recently, such profile decompos…
Channels of energy for the linear radial wave equation
Carlos Kenig, Andrew Lawrie, Baoping Liu +1
Exterior channel of energy estimates for the radial wave equation were first considered in three dimensions by Duyckaerts, the first author, and Merle, and recently for the 5-dimen…
Stable soliton resolution for exterior wave maps in all equivariance classes
Carlos Kenig, Andrew Lawrie, Baoping Liu +1
In this paper we consider finite energy, \ell-equivariant wave maps from 1+3-dimensional Minkowski space exterior to the unit ball at the origin into the 3-sphere. We impose a Diri…
Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm
Benjamin Dodson, Andrew Lawrie
In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the mode…