On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schrödinger equations
نویسنده
چکیده
The Cauchyand periodic boundary value problem for the nonlinear Schrödinger equations in n space dimensions ut − i∆u = (∇u) β , |β| = m ≥ 2, u(0) = u0 ∈ H s+1 x is shown to be locally well posed for s > sc := n 2 − 1 m−1 , s ≥ 0. In the special case of space dimension n = 1 a global L-result is obtained for NLS with the nonlinearity N(u) = ∂x(u ). The proof uses the Fourier restriction norm method.
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