Global well-posedness of the two-dimensional Benjamin equation in the energy space. (February 2019) - Chen, Wengu; Wei, Suqing; Li, Junfeng
Abstract: In this paper, the global well-posedness of the Cauchy problem for the two-dimensional Benjamin equation ∂ t u + ∂ x 3 u − ϵ H ∂ x 2 u − ∂ x − 1 ∂ y 2 u + ∂ x ( u 2 ∕ 2 ) = 0, u ( x, y, 0 ) = ϕ ( x, y ) in the energy space E 1 = { u : ‖ u ‖ L 2 + ‖ ∂ x u ‖ L 2 + ‖ ∂ x − 1 ∂ y u ‖ L 2 < ∞ } is obtained.