Global well-posedness for the Benjamin equation in low regularity

In this paper we consider the initial value problem of the Benjamin equation partial derivative(t)u + nu H(partial derivative(2)(x)u) + mu partial derivative(3)(x)u + partial derivative(x)u(2) = 0, where u : R x [0, T] bar right arrow R, and the constants nu, mu is an element of R, mu not equal 0. We use the I-method to show that it is globally well-posed in Sobolev spaces H-s(R) for s > -3/4. Moreover, we use some argument to obtain a good estimative for the lifetime of the local solution, and employ some multiplier decomposition argument to construct the almost conserved quantities. (C) 2010 Elsevier Ltd. All rights reserved.