QUALITATIVE ANALYSIS FOR A NEW GENERALIZED 2-COMPONENT CAMASSA-HOLM SYSTEM

This paper considers the Cauchy problem for a 2-component Camassa-Holm system m(t) = (um) (x) + u(x)m vm; n(t) = (un) x + u(x)n + vn; where n + m = 1/2 (u(xx) 4u), n = v(x), this model was proposed in [2] from a novel method to the Euler-Bernoulli Beam on the basis of an inhomogeneous matrix string problem. The local well-posedness in Sobolev spaces H-s (R) x Hs (R) with s > 5/2 of this system was investigated through the Kato's theory, then the blow-up criterion for this system was described by the technique on energy methods. Finally, we established the analyticity in both time and space variables of the solutions for this system with a given analytic initial data.