Zakharov system in two space dimensions. (January 2022) - Ozawa, Tohru; Tomioka, Kenta
Abstract: 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 H 2 ⊕ H 1 . The method of the construction of global solutions depends on the proof that solutions of some regularized system form a bounded sequence in H 2 ⊕ H 1 and a Cauchy sequence in H 1 ⊕ L 2 . The method of proof is independent of the compactness argument and Brezis–Gallouet inequality.