LAUSR

We study the well-posedness of the 5-th Korteweg–de Vries (KdV) equation in the space H2+s(0,r) when the initial data is drawn from H2+s(0,r) and the boundary data (h1(t),h2(t),…,h5(t)) lies in the product space Hs1(0,T),…,Hs5(0,T) for some appropriate indices s1,s2,…,s5 that depend on s. As we will see later, the natural choices of s1,s2,…,s5 are s1=(s+2)∕5, s2=(s+1)∕5, s3=s∕5, s4=(s−1)∕5, s5=(s−2)∕5. We first use contraction mapping method to obtain the local solution of the IBVP, furthermore to get the global solution by the a prior estimate.