Open AccessLocal well-posedness for the Zakharov system in dimension $ d = 2, 3 $
Author(s) -
Zijun Chen,
Shourong Wu
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021161
Subject(s) - dimension (graph theory) , mathematics , combinatorics , space (punctuation) , arithmetic , computer science , operating system
The Zakharov system in dimension \begin{document}$ d = 2,3 $\end{document} is shown to have a local unique solution for any initial values in the space \begin{document}$ H^{s} \times H^{l} \times H^{l-1} $\end{document} , where a new range of regularity \begin{document}$ (s, l) $\end{document} is given, especially at the line \begin{document}$ s-l = -1 $\end{document} . The result is obtained mainly by the normal form reduction and the Strichartz estimates.