We study the Cauchy problem for the Zakharov system in a two dimensional domain. Under natural assumptions on the data, we prove the existence and uniqueness of global solutions in H2⊕H1. The method of the construction of global solutions depends on the proof that solutions of some regularized system form a bounded sequence in H2⊕H1 and a Cauchy sequence in H1⊕L2. The method of proof is independent of the compactness argument and Brezis–Gallouet inequality.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2022 Jan|
- Global solutions
- Zakharov system
ASJC Scopus subject areas
- Applied Mathematics