Global well-posedness for the Benjamin equation in low regularity Original Research Article

In this paper we consider the initial value problem of the Benjamin equation View the MathML source∂tu+νH(∂x2u)+μ∂x3u+∂xu2=0, Turn MathJax on where u:R×[0,T]↦Ru:R×[0,T]↦R, and the constants ν,μ∈R,μ≠0ν,μ∈R,μ≠0. We use the I-method to show that it is globally well-posed in Sobolev spaces Hs(R)Hs(R) for s>−3/4s>−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.