Osaka Journal of Mathematics

Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order

Masanori Otani

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We study the well-posedness issue of the generalized Benjamin-Ono-Burgers (gBO-B) equations. We solve the initial-value problem (IVP) of the gBO-B equations with data below $L^2 (\mathbf{R})$. Our proof is based on the method of L. Molinet and F. Ribaud, which is analogous to that of J. Bourgain, and C.E. Kenig, G. Ponce, and L. Vega. It is known that such a method cannot be applied to the Benjamin-Ono equation.

Article information

Osaka J. Math., Volume 43, Number 4 (2006), 935-965.

First available in Project Euclid: 11 December 2006

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Zentralblatt MATH identifier

Primary: 35A07 35M10: Equations of mixed type 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]


Otani, Masanori. Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order. Osaka J. Math. 43 (2006), no. 4, 935--965.

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