Journal of Evolution Equations

, Volume 5, Issue 4, pp 509–527 | Cite as

The periodic Cauchy problem of the modified Hunter-Saxton equation

  • Feride Tiğlay
Original Paper

Abstract.

We prove that the periodic initial value problem for the modified Hunter-Saxton equation is locally well-posed for initial data in the space of continuously differentiable functions on the circle and in Sobolev spaces \(H^s (\mathbb{T})\) when s > 3/2. We also study the analytic regularity (both in space and time variables) of this problem and prove a Cauchy-Kowalevski type theorem. Our approach is to rewrite the equation and derive the estimates which permit application of o.d.e. techniques in Banach spaces. For the analytic regularity we use a contraction argument on an appropriate scale of Banach spaces to obtain analyticity in both time and space variables.

Mathematics Subject Classification (2000).

35Q58 35Q53 35A10 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Feride Tiğlay
    • 1
  1. 1.Department of MathematicsUniversity of New OrleansNew OrleansUSA

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