Abstract
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.
Citation
Masanori Otani. "Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order." Osaka J. Math. 43 (4) 935 - 965, December 2006.
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