Global Well-Posedness and Limit Behavior for a Higher-Order Benjamin-Ono Equation
نویسندگان
چکیده
منابع مشابه
Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation
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 t...
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We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation ut −D α xux + uxyy = uux, (t, x, y) ∈ R , 1 ≤ α ≤ 2, is locally well-posed in the spaces Es, s > 2 α − 3 4 , endowed with the norm ‖f‖Es = ‖〈|ξ| α + μ〉f̂‖L2(R2). As a consequence, we get the global wellposedness in the energy space E1/2 as soon as α > 8 5 . The proof is based ...
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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2012
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2012.683846