# Dynamics of bubbling wave maps with prescribed radiation

@article{Jendrej2019DynamicsOB, title={Dynamics of bubbling wave maps with prescribed radiation}, author={Jacek Jendrej and Andrew Lawrie and Casey Rodriguez}, journal={Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure}, year={2019} }

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 the energy of (possibly) several copies of the ground state harmonic map at the origin. If only a single bubble of energy is concentrated, the solution decomposes into a dynamically rescaled harmonic map plus a term that accounts for the energy that radiates away from the singularity. In this paper, we construct blow…

## 9 Citations

### Global, Non-Scattering Solutions to the Energy Critical Wave Maps Equation

- MathematicsCommunications in Mathematical Physics
- 2023

We consider the 1-equivariant energy critical wave maps problem with two-sphere target. Using a method based on matched asymptotic expansions, we construct infinite time relaxation, blow-up, and…

### Sharp universal rate for stable blow-up of corotational wave maps

- Mathematics
- 2022

We consider the energy-critical (corotational) 1-equivariant wave maps into the two-sphere. By the seminal work [53] of Raphaël and Rodnianski, there is an open set of initial data whose…

### Soliton resolution for the radial quadratic wave equation in six space dimensions

- Mathematics
- 2022

. We consider the quadratic semilinear wave equation in six dimensions. This energy critical problem admits a ground state solution, which is the unique (up to scaling) positive stationary solution.…

### Global, non-scattering solutions to the energy critical Yang–Mills problem

- Mathematics
- 2019

We consider the Yang-Mills problem on $\mathbb{R}^{1+4}$ with gauge group $SO(4)$. In an appropriate equivariant reduction, this Yang-Mills problem reduces to a single scalar semilinear wave…

### Multi‐bubble blowup of focusing energy‐critical wave equation in dimension 6

- MathematicsMathematical Methods in the Applied Sciences
- 2022

We consider the energy‐critical focusing wave equation ∂t2u(t,x)−Δu(t,x)=u(t,x)u(t,x),t∈ℝ,x∈ℝ6 , and we prove the existence of infinite time blowup at the vertices of any regular polyhedron. The…

### Non-flat conformal blow-up profiles for the 1D critical nonlinear Schr\"odinger equation

- Mathematics
- 2022

For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a non-flat blow-up…

### Construction of excited multi-solitons for the focusing 4D cubic wave equation

- MathematicsJournal of Functional Analysis
- 2022

### Blow-up dynamics for smooth finite energy radial data solutions to the self-dual Chern-Simons-Schr\"odinger equation

- Mathematics
- 2020

We consider the finite-time blow-up dynamics of solutions to the self-dual Chern-Simons-Schrodinger (CSS) equation (also referred to as the Jackiw-Pi model) near the radial soliton $Q$ with the least…

### Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line

- MathematicsDuke Mathematical Journal
- 2022

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 antikinks, which are…

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