View in EDS

Nonexistence of Minimal Mass Blow-Up Solution for the 2D Cubic Zakharov–Kuznetsov Equation.

Saved in:
Bibliographic Details
Title: Nonexistence of Minimal Mass Blow-Up Solution for the 2D Cubic Zakharov–Kuznetsov Equation.
Authors: Chen, Gong1 (AUTHOR) gc@math.gatech.edu, Lan, Yang2 (AUTHOR) lanyang@mail.tsinghua.edu.cn, Yuan, Xu3 (AUTHOR) xu.yuan@amss.ac.cn
Source: SIAM Journal on Mathematical Analysis. 2025, Vol. 57 Issue 6, p5950-5975. 26p.
Subjects: Modulation theory, Lyapunov functions, Partial differential equations, Ordinary differential equations, Function spaces, Mass (Physics)
Abstract: For the 2D cubic (mass-critical) Zakharov–Kuznetsov equation, \(\partial_t\phi +\partial_{x_1} (\Delta \phi +\phi^3)=0\) , \((t,x)\in [0,\infty)\times \mathbb{R}^{2}\) , we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel–Merle–Raphaël [J. Eur. Math. Soc. (JEMS), 17 (2015), pp. 1855–1925] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 189326336
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Nonexistence of Minimal Mass Blow-Up Solution for the 2D Cubic Zakharov–Kuznetsov Equation.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Gong%22">Chen, Gong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gc@math.gatech.edu</i><br /><searchLink fieldCode="AR" term="%22Lan%2C+Yang%22">Lan, Yang</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> lanyang@mail.tsinghua.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yuan%2C+Xu%22">Yuan, Xu</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> xu.yuan@amss.ac.cn</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Mathematical+Analysis%22">SIAM Journal on Mathematical Analysis</searchLink>. 2025, Vol. 57 Issue 6, p5950-5975. 26p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Modulation+theory%22">Modulation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Function+spaces%22">Function spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mass+%28Physics%29%22">Mass (Physics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: For the 2D cubic (mass-critical) Zakharov–Kuznetsov equation, \(\partial_t\phi +\partial_{x_1} (\Delta \phi +\phi^3)=0\) , \((t,x)\in [0,\infty)\times \mathbb{R}^{2}\) , we prove that there exist no finite/infinite time blow-up solution with minimal mass in the energy space. This nonexistence result is in contrast to the one obtained by Martel–Merle–Raphaël [J. Eur. Math. Soc. (JEMS), 17 (2015), pp. 1855–1925] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. The proof relies on a refined ODE argument related to the modulation theory and a modified energy-virial Lyapunov functional with a monotonicity property. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=189326336
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1137/24M1716483
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 5950
    Subjects:
      – SubjectFull: Modulation theory
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Ordinary differential equations
        Type: general
      – SubjectFull: Function spaces
        Type: general
      – SubjectFull: Mass (Physics)
        Type: general
    Titles:
      – TitleFull: Nonexistence of Minimal Mass Blow-Up Solution for the 2D Cubic Zakharov–Kuznetsov Equation.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Chen, Gong
      – PersonEntity:
          Name:
            NameFull: Lan, Yang
      – PersonEntity:
          Name:
            NameFull: Yuan, Xu
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 11
              Text: 2025
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 00361410
          Numbering:
            – Type: volume
              Value: 57
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: SIAM Journal on Mathematical Analysis
              Type: main
ResultId 1