The Cauchy Problem for the CH2 System

Doctoral Dissertation

Abstract

For Sobolev exponent s > 5=2, it is shown that the data-to-solution map for the2-component Camassa-Holm system is continuous from Hs x Hs􀀀-1 into C([0; T];Hs x Hs􀀀-1) but not uniformly continuous. The proof of non-uniform dependence on the initial data is based on the method of approximate solutions, delicate commutator and multiplier estimates, and well-posedness results for the solution and its lifespan. Also, the solution map is Holder continuous if the Hs x Hs-􀀀1 norm is replaced by an Hr x Hr􀀀-1 norm for 0 r < s.

Attributes

Attribute NameValues
URN
  • etd-03162015-154155

Author Ryan Cole Thompson
Advisor Alex Himonas
Contributor Alex Himonas, Committee Chair
Contributor Gerard Misiolek, Committee Member
Contributor Yongtao Zhang, Committee Member
Contributor Alan Lindsay, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2015-03-03

Submission Date 2015-03-16
Country
  • United States of America

Subject
  • approximate solutions

  • well-posedness

  • integrability

  • initial value problem

  • Sobolev spaces

  • H�older continuity

  • non-uniform dependence on initial data

  • multiplier estimate.

  • commutator estimate

  • peakons

  • continuity properties

  • 2-component Camassa-Holm system equation

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units

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