Well-posed solutions of the third order Benjamin-Ono equation in weighted Sobolev spaces

Xueshang Feng

doi:10.36045/bbms/1105736872

Well-posed solutions of the third order Benjamin-Ono equation in weighted Sobolev spaces

Xueshang Feng^*

^*Corresponding author for this work

Chinese Academy of Sciences

Research output: Contribution to journal › Review article › peer-review

3 Scopus citations

Abstract

Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces H^s_γ = H^s ∩ L²_γ, where s > 3, γ ≥ 0. The result is the proof of well-posedness of the afore mentioned problem in H^sγ, s > 3, γ ∈ [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of auxiliary functions.

Original language	English
Pages (from-to)	525-537
Number of pages	13
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	4
Issue number	4
DOIs	https://doi.org/10.36045/bbms/1105736872
State	Published - Sep 1997
Externally published	Yes

Keywords

Global well-posedness
Initial value problem
The third order BO equation
Weighted Sobolev spaces

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10.36045/bbms/1105736872

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abstract = "Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces Hsγ = Hs ∩ L2γ, where s > 3, γ ≥ 0. The result is the proof of well-posedness of the afore mentioned problem in Hsγ, s > 3, γ ∈ [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of auxiliary functions.",

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AU - Feng, Xueshang

PY - 1997/9

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N2 - Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces Hsγ = Hs ∩ L2γ, where s > 3, γ ≥ 0. The result is the proof of well-posedness of the afore mentioned problem in Hsγ, s > 3, γ ∈ [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of auxiliary functions.

AB - Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces Hsγ = Hs ∩ L2γ, where s > 3, γ ≥ 0. The result is the proof of well-posedness of the afore mentioned problem in Hsγ, s > 3, γ ∈ [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of auxiliary functions.

KW - Global well-posedness

KW - Initial value problem

KW - The third order BO equation

KW - Weighted Sobolev spaces

UR - https://www.scopus.com/pages/publications/0031231636

U2 - 10.36045/bbms/1105736872

DO - 10.36045/bbms/1105736872

M3 - 文献综述

AN - SCOPUS:0031231636

SN - 1370-1444

VL - 4

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EP - 537

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 4

ER -

Well-posed solutions of the third order Benjamin-Ono equation in weighted Sobolev spaces

Abstract

Keywords

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