Abstract
We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.
| Original language | English |
|---|---|
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | Journal of Functional Analysis |
| Volume | 219 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2005 Feb 1 |
| Externally published | Yes |
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Keywords
- Endpoint Strichartz estimates
- Klein-Gordon equation
- Nonlinear Dirac equation
ASJC Scopus subject areas
- Analysis
Cite this
Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation. / Machihara, Shuji; Nakamura, Makoto; Nakanishi, Kenji; Ozawa, Tohru.
In: Journal of Functional Analysis, Vol. 219, No. 1, 01.02.2005, p. 1-20.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Endpoint Strichartz estimates and global solutions for the nonlinear Dirac equation
AU - Machihara, Shuji
AU - Nakamura, Makoto
AU - Nakanishi, Kenji
AU - Ozawa, Tohru
PY - 2005/2/1
Y1 - 2005/2/1
N2 - We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.
AB - We prove endpoint Strichartz estimates for the Klein-Gordon and wave equations in mixed norms on the polar coordinates in three spatial dimensions. As an application, global wellposedness of the nonlinear Dirac equation is shown for small data in the energy class with some regularity assumption for the angular variable.
KW - Endpoint Strichartz estimates
KW - Klein-Gordon equation
KW - Nonlinear Dirac equation
UR - http://www.scopus.com/inward/record.url?scp=10344222722&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=10344222722&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2004.07.005
DO - 10.1016/j.jfa.2004.07.005
M3 - Article
AN - SCOPUS:10344222722
VL - 219
SP - 1
EP - 20
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -