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2001 On a nonlinear dispersive equation with time-dependent coefficients
Corinne Laurey
Adv. Differential Equations 6(5): 577-612 (2001). DOI: 10.57262/ade/1357141856


As a first step, we consider an evolution linear problem, the symbol of which is a real polynomial of degree three with time-dependent coefficients. We get for this problem smoothing effects known when these coefficients are constant. In particular, by using the theory of Calderón-Zygmund operators and the David and Journé T1 Theorem, we establish a local smoothing effect on the solution of the linear problem. In a second step, we study a nonlinear dispersive equation the linear part of which is the one studied above. We use the previous smoothing properties and a regularization method to establish that the Cauchy problem is locally well-posed in the Sobolev spaces $H^s(\mathbb R)$ for $s>3/4$.


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Corinne Laurey. "On a nonlinear dispersive equation with time-dependent coefficients." Adv. Differential Equations 6 (5) 577 - 612, 2001.


Published: 2001
First available in Project Euclid: 2 January 2013

zbMATH: 1003.35118
MathSciNet: MR1826722
Digital Object Identifier: 10.57262/ade/1357141856

Primary: 35Q55
Secondary: 35B30 , 35B35 , 35Q53 , 35Q60

Rights: Copyright © 2001 Khayyam Publishing, Inc.


Vol.6 • No. 5 • 2001
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