Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation
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چکیده
In this paper, we prove that the Cauchy problem associated to the following higher-order Benjamin-Ono equation (0.1) ∂tv − bH∂ 2 x v − aǫ∂ x v = cv∂xv − dǫ∂x(vH∂xv +H(v∂xv)), is globally well-posed in the energy space H(R). Moreover, we study the limit behavior when the small positive parameter ǫ tends to zero and show that, under a condition on the coefficients a, b, c and d, the solution vǫ to (0.1) converges to the corresponding solution of the Benjamin-Ono equation.
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تاریخ انتشار 2011