Well-posedness for a higher-order Benjamin–Ono equation
نویسندگان
چکیده
منابع مشابه
Well-posedness for a Higher-order Benjamin-ono Equation
In this paper we prove that the initial value problem associated to the following higher-order Benjamin-Ono equation ∂tv − bH∂ xv + a∂ xv = cv∂xv − d∂x(vH∂xv + H(v∂xv)), where x, t ∈ R, v is a real-valued function, H is the Hilbert transform, a ∈ R, b, c and d are positive constants, is locally well-posed for initial data v(0) = v0 ∈ H(R), s ≥ 2 or v0 ∈ H(R) ∩ L(R; xdx), k ∈ Z+, k ≥ 2.
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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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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2011
ISSN: 0022-0396
DOI: 10.1016/j.jde.2010.08.022