Critical local well-posedness for NLS with non-algebraic nonlinearity |u|^a u is proved on tori for a > 4/d, using a new function space and bilinear estimate.
Operator-valued Fourier multipliers, v ector-valued Besov spaces, and appli- cations
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Critical local well-posedness of the nonlinear Schr\"odinger equation on the torus
Critical local well-posedness for NLS with non-algebraic nonlinearity |u|^a u is proved on tori for a > 4/d, using a new function space and bilinear estimate.