• Corpus ID: 225062357

Continuous time soliton resolution for two-bubble equivariant wave maps.

  title={Continuous time soliton resolution for two-bubble equivariant wave maps.},
  author={Jacek Jendrej and Andrew Lawrie},
  journal={arXiv: Analysis of PDEs},
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 sequence of times, into a superposition of at most two rescaled harmonic maps (bubbles) and radiation, then such a decomposition holds for continuous time. If the equivariance degree equals one or two, we deduce, as a consequence of sequential soliton resolution results of Cote, and Jia and Kenig, that any… 

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

. 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.

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

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

Wave maps into the sphere

  • C. Kenig
  • Mathematics
    Revista de la Unión Matemática Argentina
  • 2022
In this note we discuss some geometric analogs of the classical harmonic functions on Rn and their associated evolutions. Harmonic functions are ubiquitous in mathematics, with applications arising



An asymptotic expansion of two-bubble wave maps in high equivariance classes

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 the two-sphere

Construction of two-bubble solutions for energy-critical wave equations

  • Jacek Jendrej
  • Physics, Mathematics
    American Journal of Mathematics
  • 2019
Abstract:We construct pure two-bubbles for some energy-critical wave equations, that is solutions which in one time direction approach a superposition of two stationary states both centered at the

On the Soliton Resolution for Equivariant Wave Maps to the Sphere

We consider finite energy corotational wave maps with target manifold S2 . We prove that for a sequence of times, they decompose as a sum of decoupled harmonic maps in the light cone, and a smooth

Global, Non-scattering solutions to the energy critical wave maps equation

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

Asymptotic decomposition for semilinear Wave and equivariant wave map equations

abstract:In this paper we give a unified proof to the soliton resolution conjecture along a sequence of times, for the semilinear focusing energy critical wave equations in the radial case and two

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from ℝ2+1→S2 of the form $u(t,r)=Q(\lambda(t)r)+\mathcal{R}(t,r)$ where u is the polar angle on the

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

We consider $1$-equivariant wave maps from ${\Bbb R}^{1+2}\to{\Bbb S}^2$. For wave maps of topological degree zero we prove global existence and scattering for energies below twice the energy of

Equivariant wave maps in two space dimensions

Singularities of corotational wave maps from (1 + 2)‐dimensional Minkowski space into a surface N of revolution after a suitable rescaling give rise to nonconstant corotational harmonic maps from 𝕊2

On the stability of blowup solutions for the critical corotational wave-map problem

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the

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

We consider the energy-critical wave maps equation $$\mathbb {R}^{1+2} \rightarrow \mathbb {S}^2$$R1+2→S2 in the equivariant case, with equivariance degree $$k \ge 2$$k≥2. It is known that initial