Cubic NLW/NLKG on R4: Difference between revisions
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* Scaling is <math>s_c = 1</math>. | * Scaling is <math>s_c = 1</math>. | ||
* LWP for <math>s \geq 1</math> by Strichartz estimates (see e.g. [[Bibliography#LbSo1995|LbSo1995]]; earlier references exist) | * LWP for <math>s \geq 1</math> by Strichartz estimates (see e.g. [[Bibliography#LbSo1995|LbSo1995]]; earlier references exist) | ||
Revision as of 01:28, 29 July 2006
- Scaling is .
- LWP for by Strichartz estimates (see e.g. LbSo1995; earlier references exist)
- When the time of existence depends on the profile of the data and not just on the norm.
- One has strong uniqueness in the energy class [Pl-p5], FurPlTer2001. This argument extends to other energy-critical and sub-critical powers in dimensions 4 and higher.
- For one has instantaneous blowup in the focusing case, and unbounded growth of norms in the defocusing case [CtCoTa-p2]
- GWP for in the defocussing case SaSw1994 (see also Gl1990, Gl1992, Sw1988, Sw1992, BaSa1998, BaGd1997).
- In the focussing case there is blowup from large data by the ODE method.
