Differential and Integral Equations

Norm inflation for equations of KdV type with fractional dispersion

Vera Mikyoung Hur

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Abstract

We demonstrate norm inflation for nonlinear nonlocal equations, which extend the Korteweg-de Vries equation to permit fractional dispersion, in the periodic and non-periodic settings. That is, an initial datum is smooth and arbitrarily small in a Sobolev space but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time.

Article information

Source
Differential Integral Equations, Volume 31, Number 11/12 (2018), 833-850.

Dates
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1537840871

Mathematical Reviews number (MathSciNet)
MR3857866

Zentralblatt MATH identifier
06986980

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35R11: Fractional partial differential equations 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Hur, Vera Mikyoung. Norm inflation for equations of KdV type with fractional dispersion. Differential Integral Equations 31 (2018), no. 11/12, 833--850. https://projecteuclid.org/euclid.die/1537840871


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