Global well-posedness and inviscid limit for the generalized Benjamin-Ono-Burgers equation

This paper deals with the Cauchy problem for the generalized Benjamin-Ono-Burgers equation partial derivative(t)u + H partial derivative(2)(x) - nu u(xx) + partial derivative x(u(k+1)/(k + 1)) = 0, k >= 4, where H denotes Hilbert transform. We obtain its global well-posedness results in Besov Spaces if k >= 4 and the initial data in. (B) over dot(2,1)(sk),1 are sufficiently small, where s(k) := 1/2 - 1/k corresponds to the critical scaling regularity index. Furthermore, we prove its global well-posedness and inviscid limit behavior in Sobolev spaces.