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

School of Mathematics and Statistics

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

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2141-2190
Number of pages	50
Journal	Communications in Mathematical Sciences
Volume	17
Issue number	8
DOIs	https://doi.org/10.4310/CMS.2019.v17.n8.a4
Publication status	Published - 2019

Keywords

Global regularity
Modulus of continuity
Singularity
Surface wave equation
Whitham equation

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10.4310/CMS.2019.v17.n8.a4

Cite this

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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",

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AU - Miao, Qianyun

AU - Xue, Liutang

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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

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

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SN - 1539-6746

VL - 17

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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

Abstract

Keywords

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