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
N1 - Funding Information:
∗Corresponding author. Department of Mathematics, Shimane University, Matsue, 690-8504, Japan. E-mail addresses: machihara@math.shimane-u.ac.jp (S. Machihara), m-nakamu@math.is.tohoku.ac.jp (M. Nakamura), n-kenji@math.nagoya-u.ac.jp (K. Nakanishi). 1K.N. was partly supported by JSPS Postd octoral Fellowships for Research Abroad (2001–2003).
Copyright:
Copyright 2004 Elsevier B.V., All rights reserved.
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
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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 -