Issue |
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|
|
---|---|---|
Article Number | 12 | |
Number of page(s) | 27 | |
DOI | https://doi.org/10.1051/cocv/2021012 | |
Published online | 11 March 2021 |
Kato smoothing properties of a class of nonlinear dispersive wave equations on a periodic domain*
1
Department of Mathematics, Virginia Polytechnic Institute and State University,
Blacksburg,
VA
24061, USA.
2
Department of Mathematics, University of California at Riverside,
Riverside,
CA
92521, USA.
3
Department of Mathematical Sciences, University of Cincinnati,
Cincinnati,
Ohio
45221, USA.
** Corresponding author: zhangb@ucmail.uc.edu
Received:
10
August
2020
Accepted:
23
January
2021
The solutions of the Cauchy problem of the KdV equation on a periodic domain 𝕋,
possess neither the sharp Kato smoothing property,
nor the Kato smoothing property,
Considered in this article is the Cauchy problem of the following dispersive equations posed on the periodic domain 𝕋, (See Eq. (1) below)
where g ∈ C∞(𝕋) is a real value function with the support
It is shown that
(1) if ω ≠ ∅, then the solutions of the Cauchy problem (1) possess the Kato smoothing property;
(2) if g is a nonzero constant function, then the solutions of the Cauchy problem (1) possess the sharp Kato smoothing property.
Mathematics Subject Classification: 35B65 / 35Q53 / 35K45
Key words: Kato smoothing property / sharp Kato smoothing property / KdV equation / KdV-Burgers equation
© EDP Sciences, SMAI 2021
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