In this paper we study the well-posedness of Cauchy problem for a Boussinesq system formed by two Kortewegde Vries equations coupled through the linear part and the non-linear terms. First we proof its local well-posednessin the Sobolev spaces Hs (R) x Hs (R), s > -3/4, using the bilinear estimate established by Kenig, Ponce and Vega in the Fourier transform restriction spaces [4, 12]. After, we prove the global well-posedness in Hs (R) x Hs (R) for s > -3/10, our proof proceeds by the method of almost conservation laws, sometimes called the “I-method”[5, 6].

In this paper we study the well-posedness of Cauchy problem for a Boussinesq system formed by two Kortewegde Vries equations coupled through the linear part and the non-linear terms. First we proof its local well-posednessin the Sobolev spaces Hs (R) x Hs (R), s > -3/4, using the bilinear estimate established by Kenig, Ponce and Vega in the Fourier transform restriction spaces [4, 12]. After, we prove the global well-posedness in Hs (R) x Hs (R) for s > -3/10, our proof proceeds by the method of almost conservation laws, sometimes called the “I-method”[5, 6].