Abstract
We prove the weighted Strichartz estimates for the wave equation in even space dimensions with radial symmetry in space. Although the odd space dimensional cases have been treated in our previous paper [5], the lack of the Huygens principle prevents us from a similar treatment in even space dimensions. The proof is based on the two explicit representations of solutions due to Rammaha [11] and Takamura [14] and to Kubo-Kubota [6]. As in the odd space dimensional cases [5], we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.
| Original language | English |
|---|---|
| Pages (from-to) | 747-764 |
| Number of pages | 18 |
| Journal | Mathematische Zeitschrift |
| Volume | 247 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2004 Aug |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
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Weighted Strichartz estimates for the wave equation in even space dimensions. / Kato, Jun; Ozawa, Tohru.
In: Mathematische Zeitschrift, Vol. 247, No. 4, 08.2004, p. 747-764.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Weighted Strichartz estimates for the wave equation in even space dimensions
AU - Kato, Jun
AU - Ozawa, Tohru
PY - 2004/8
Y1 - 2004/8
N2 - We prove the weighted Strichartz estimates for the wave equation in even space dimensions with radial symmetry in space. Although the odd space dimensional cases have been treated in our previous paper [5], the lack of the Huygens principle prevents us from a similar treatment in even space dimensions. The proof is based on the two explicit representations of solutions due to Rammaha [11] and Takamura [14] and to Kubo-Kubota [6]. As in the odd space dimensional cases [5], we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.
AB - We prove the weighted Strichartz estimates for the wave equation in even space dimensions with radial symmetry in space. Although the odd space dimensional cases have been treated in our previous paper [5], the lack of the Huygens principle prevents us from a similar treatment in even space dimensions. The proof is based on the two explicit representations of solutions due to Rammaha [11] and Takamura [14] and to Kubo-Kubota [6]. As in the odd space dimensional cases [5], we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.
UR - http://www.scopus.com/inward/record.url?scp=3543011986&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=3543011986&partnerID=8YFLogxK
U2 - 10.1007/s00209-003-0645-5
DO - 10.1007/s00209-003-0645-5
M3 - Article
AN - SCOPUS:3543011986
VL - 247
SP - 747
EP - 764
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 4
ER -