On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation

.In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on \(T^2\) with general data in the critical Sobolev space \(H1/2 (T^2)\). We show that if a solution remains bounded in \(H1/2 (T^2)\) in its maximal interval of existence, then the solution exists globally in time.Keywordsnonlinear Schrödinger equationglobal well-posednesscompact manifoldMSC codes35Q5535R0137K0637L50