Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

By Pierre Raphael, Igor Rodnianski. Publications mathématiques (Bures-sur-Yvette), 2009

221 citations recorded by the source corpus.

We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the S2 target in all homotopy classes and for the critical equivariant SO(4) Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/668e53dfb2e1dc8a3ce8288cddf5bd1193c4fb13

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. F. Merle
2. Pierre Raphael
3. Yvan Martel
4. Carlos E. Kenig
5. Jérémie Szeftel
6. Raphael Cote
7. Hatem Zaag
8. Thomas Duyckaerts

In Nuclear and High Energy Physics

1. Yvan Martel
2. F. Merle
3. Carlos E. Kenig
4. Hao Jia
5. Pierre Raphael
6. Jérémie Szeftel

In Statistical and Nonlinear Physics

1. F. Merle
2. Pierre Raphael
3. Carlos E. Kenig
4. Yvan Martel
5. Jérémie Szeftel
6. Hatem Zaag
7. Raphael Cote
8. Hao Jia

Citations in the corpus

• Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton (2014, methodology): “A related strategy originated in [24], [32], [33] and [39], but is implemented here in a new optimal way.”
• Blow up for the critical gKdV equation II: minimal mass dynamics (2012, methodology): “In Part I [29], we have revisited the blow up analysis in light of recent developments related to blow up for the mass critical Schrödinger equation [35]–[40] and energy critical geometrical equations [41], [46], [47].”
• On collapsing ring blow up solutions to the mass supercritical NLS (2012, methodology): “ly and only depend on Tp,q, c1,p,q and c2,p,q for p+q≤ j+l−1. The invertibility of (3.17) requires according to (3.16) to manufacture the orthogonality conditions (h(1) j ,Q ′) = (h(2) j ,Q) = 0, see [37] for related issues. We also need to track the decay in space of the associated solution in a sh”
• Asymptotic decomposition for semilinear Wave and equivariant wave map equations (2015, methodology): “We refer to [29] for more discussion of the physical background of this equation.”