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Article Dans Une Revue Communications in Partial Differential Equations Année : 2012

Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation

Résumé

In this paper, we prove that the Cauchy problem associated to the following higher-order Benjamin-Ono equation $$ \partial_tv-b\mathcal{H}\partial^2_xv- a\epsilon \partial_x^3v=cv\partial_xv-d\epsilon \partial_x(v\mathcal{H}\partial_xv+\mathcal{H}(v\partial_xv)), $$ is globally well-posed in the energy space $H^1(\mathbb R)$. Moreover, we study the limit behavior when the small positive parameter $\epsilon$ tends to zero and show that, under a condition on the coefficients $a$, $b$, $c$ and $d$, the solution $v_{\epsilon}$ to this equation converges to the corresponding solution of the Benjamin-Ono equation.
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Dates et versions

hal-00637981 , version 1 (03-11-2011)

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Luc Molinet, Didier Pilod. Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation. Communications in Partial Differential Equations, 2012, 37 (11), pp.2050-2080. ⟨hal-00637981⟩
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