Differential and Integral Equations

A bilinear estimate with application to the sixth-order Boussinesq equation

Amin Esfahani and Hongwei Wang

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In this work, we study the Cauchy problem of the sixth-order Boussinesq equation. We shall use the $[k; Z]$-multiplier norm method to get a bilinear estimate on nonlinear term, and the local well-posedness on $H^s(\mathbb{R})$ is obtained for $s\gt-\frac{3}{4}$.

Article information

Differential Integral Equations, Volume 27, Number 5/6 (2014), 401-414.

First available in Project Euclid: 3 April 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics 76B55: Internal waves 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35G25: Initial value problems for nonlinear higher-order equations 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]


Esfahani, Amin; Wang, Hongwei. A bilinear estimate with application to the sixth-order Boussinesq equation. Differential Integral Equations 27 (2014), no. 5/6, 401--414. https://projecteuclid.org/euclid.die/1396558088

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