Regularity and singularity results for the dissipative whitham equation and related surface wave equations

Qianyun Miao; Liutang Xue

doi:10.4310/CMS.2019.v17.n8.a4

Regularity and singularity results for the dissipative whitham equation and related surface wave equations

Qianyun Miao
, Liutang Xue

数学学院

Peking University
Beijing Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

We consider the cauchy problem for the whitham equation and related surface wave equations with (fractional) dissipation. we prove global regularity results at the subcritical and critical dissipative cases by applying the method of modulus of continuity, and we show a finite-time singularity result at the supercritical dissipative case.

源语言	英语
页（从-至）	2141-2190
页数	50
期刊	Communications in Mathematical Sciences
卷	17
期	8
DOI	https://doi.org/10.4310/CMS.2019.v17.n8.a4
出版状态	已出版 - 2019

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10.4310/CMS.2019.v17.n8.a4

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title = "Regularity and singularity results for the dissipative whitham equation and related surface wave equations",

abstract = "We consider the cauchy problem for the whitham equation and related surface wave equations with (fractional) dissipation. we prove global regularity results at the subcritical and critical dissipative cases by applying the method of modulus of continuity, and we show a finite-time singularity result at the supercritical dissipative case.",

keywords = "Global regularity, Modulus of continuity, Singularity, Surface wave equation, Whitham equation",

author = "Qianyun Miao and Liutang Xue",

note = "Publisher Copyright: {\textcopyright} 2019 International Press.",

year = "2019",

doi = "10.4310/CMS.2019.v17.n8.a4",

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T1 - Regularity and singularity results for the dissipative whitham equation and related surface wave equations

AU - Miao, Qianyun

AU - Xue, Liutang

PY - 2019

Y1 - 2019

N2 - We consider the cauchy problem for the whitham equation and related surface wave equations with (fractional) dissipation. we prove global regularity results at the subcritical and critical dissipative cases by applying the method of modulus of continuity, and we show a finite-time singularity result at the supercritical dissipative case.

AB - We consider the cauchy problem for the whitham equation and related surface wave equations with (fractional) dissipation. we prove global regularity results at the subcritical and critical dissipative cases by applying the method of modulus of continuity, and we show a finite-time singularity result at the supercritical dissipative case.

KW - Global regularity

KW - Modulus of continuity

KW - Singularity

KW - Surface wave equation

KW - Whitham equation

UR - https://www.scopus.com/pages/publications/85080860050

U2 - 10.4310/CMS.2019.v17.n8.a4

DO - 10.4310/CMS.2019.v17.n8.a4

M3 - Article

AN - SCOPUS:85080860050

SN - 1539-6746

VL - 17

SP - 2141

EP - 2190

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

IS - 8

ER -

Regularity and singularity results for the dissipative whitham equation and related surface wave equations

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