Differential and Integral Equations

On the regularity of the flow map associated with the 1D cubic periodic Half-Wave equation

Vladimir Georgiev, Nikolay Tzvetkov, and Nicola Visciglia

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Abstract

We prove that the solution map associated with the $1D$ half-wave cubic equation in the periodic setting cannot be uniformly continuous on bounded sets of the periodic Sobolev spaces $H^s$ with $s\in ( \frac 14 , \frac 12 )$.

Article information

Source
Differential Integral Equations Volume 29, Number 1/2 (2016), 183-200.

Dates
First available in Project Euclid: 24 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1448323259

Mathematical Reviews number (MathSciNet)
MR3450755

Zentralblatt MATH identifier
06562173

Subjects
Primary: 35B65: Smoothness and regularity of solutions 35B20: Perturbations 35B45: A priori estimates

Citation

Georgiev, Vladimir; Tzvetkov, Nikolay; Visciglia, Nicola. On the regularity of the flow map associated with the 1D cubic periodic Half-Wave equation. Differential Integral Equations 29 (2016), no. 1/2, 183--200. https://projecteuclid.org/euclid.die/1448323259.


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