Journal article
Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions
Communications in partial differential equations, Vol.38(4), pp.575-607
04/03/2013
DOI: 10.1080/03605302.2012.756520
Abstract
In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ℝ × ℝ
d
with d ≥ 6. We prove the stability of solutions under the weak condition that the perturbation of the linear flow is small in certain space-time norms. As a by-product of our stability analysis, we also prove local well-posedness of solutions for which we only assume the smallness of the linear evolution. These results provide essential technical tools that can be applied towards obtaining the extension to high dimensions of the analysis of Kenig and Merle [
17
] of the dynamics of the focusing (NLW) below the energy threshold. By employing refined paraproduct estimates we also prove unconditional uniqueness of solutions for d ≥ 6 in the natural energy class. This extends an earlier result by Planchon [
26
].
Details
- Title: Subtitle
- Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions
- Creators
- Aynur Bulut - Institute for Advanced StudyMagdalena Czubak - Binghamton UniversityDong Li - University of British ColumbiaNataša Pavlović - The University of Texas at AustinXiaoyi Zhang - Chinese Academy of Sciences
- Resource Type
- Journal article
- Publication Details
- Communications in partial differential equations, Vol.38(4), pp.575-607
- DOI
- 10.1080/03605302.2012.756520
- ISSN
- 0360-5302
- eISSN
- 1532-4133
- Publisher
- Taylor & Francis Group
- Language
- English
- Date published
- 04/03/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9984240773502771
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