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@WillieWong I know that the method presented in Tao's book is well designed for linear (and semilinear) equations, but I do not know any other method in order to find Morawetz identities. Even if the local well posedness is not easy one may expect a morawetz identity because this equation really looks like a wave equation, for which Morawetz identities hold. Maybe this is a bad heuristic, but in my opinion finding a Morawetz identity was not fatally bounded to fail !
