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2005 A bilinear Airy-estimate with application to gKdV-3
Axel Grünrock
Differential Integral Equations 18(12): 1333-1339 (2005).

Abstract

The Fourier restriction norm method is used to show local wellposedness for the Cauchy-Problem \[u_t + u_{xxx} + (u^4)_x=0,\hspace{1cm}u(0)=u_0 \in H^s_x({\bf R}), \,\,\,s>-\tfrac{1}{6}\] for the generalized Korteweg-deVries equation of order three, for short gKdV-3. For real-valued data $u_0 \in L^2_x({\bf R})$ global wellposedness follows by the conservation of the $L^2$ norm. The main new tool is a bilinear estimate for solutions of the Airy-equation.

Citation

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Axel Grünrock. "A bilinear Airy-estimate with application to gKdV-3." Differential Integral Equations 18 (12) 1333 - 1339, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35412
MathSciNet: MR2174975

Subjects:
Primary: 35Q53
Secondary: 35B30

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 12 • 2005
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