L. Farah

activity

20082026

most citedLocal solutions in Sobolev spaces with negative indices for the "good" Boussinesq equation

91 citations · 311 across the 34 of their papers we have counts for

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Showing 2010 · math.APShow all

3 papers · 2 filters

math.AP2010

Local well-posedness for the Sixth-Order Boussinesq Equation

Luiz Gustavo Farah, Amin Esfahani

This work studies the local well-posedness of the initial-value problem for the nonlinear sixth-order Boussinesq equation $u_{tt} = u_{xx} + β u_{xxxx} + u_{xxxxxx} + (u^{2})_{xx}$ , where $β=…

math.AP2010

Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces

Luiz Gustavo Farah, Hongwei Wang

We show that the Cauchy problem for the defocusing generalized Boussinesq equation $u_{tt} - u_{xx} + u_{xxxx} - (∣ u ∣^{2 k} u)_{xx} = 0$ , $k \geq 1$ , on the real line is globally well-posed in…

math.AP2010

The supercritical generalized KdV equation: Global well-posedness in the energy space and below

Luiz Gustavo Farah, Felipe Linares, Ademir Pastor

We consider the generalized Korteweg-de Vries (gKdV) equation $\partial_{t} u + \partial_{x}^{3} u + μ \partial_{x} (u^{k + 1}) = 0$ , where $k \geq 5$ is an integer number and $μ = \pm 1$ . In the focusing…