Zakharov system in two space dimensions

Tohru Ozawa; Kenta Tomioka

doi:10.1016/j.na.2021.112532

Zakharov system in two space dimensions

Tohru Ozawa^*, Kenta Tomioka

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 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.

Original language	English
Article number	112532
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	214
DOIs	https://doi.org/10.1016/j.na.2021.112532
Publication status	Published - 2022 Jan

Keywords

Global solutions
Zakharov system

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2021.112532

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title = "Zakharov system in two space dimensions",

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 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.",

keywords = "Global solutions, Zakharov system",

author = "Tohru Ozawa and Kenta Tomioka",

note = "Funding Information: We are grateful to referees for important remarks. This work is partially supported by Grant-in-Aid for Scientific Research (A) 19H00644 , JSPS. Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2022",

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doi = "10.1016/j.na.2021.112532",

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AU - Ozawa, Tohru

AU - Tomioka, Kenta

N1 - Funding Information: We are grateful to referees for important remarks. This work is partially supported by Grant-in-Aid for Scientific Research (A) 19H00644 , JSPS. Publisher Copyright: © 2021 Elsevier Ltd

PY - 2022/1

Y1 - 2022/1

N2 - 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.

AB - 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.

KW - Global solutions

KW - Zakharov system

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 112532

ER -

Zakharov system in two space dimensions

Abstract

Keywords

ASJC Scopus subject areas

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