Symplectic flow for the square root of the negative Laplacian

The paper is concerned with symplectic flow for the square root of the negative Laplacian, which is motivated when studying a one-dimensional model about ferromagnetic thin film without Gilbert damping term (only Gyromagnetic term remained) derived from the stationary model of A. DeSimone, R.V. Kohn, S. Müller and F. Otto. Existence of weak solution to the model is proved by viscosity approximation and commutator estimate.