Probabilistic local wellposedness of 1D quintic NLS below L2 (R)
We consider the Cauchy problem of the nonlinear Schrödinger equation i∂ t u+∂ x 2 u±u
5= 0 on the real line, which is L 2-critical. We prove the local well-posedness of the initial
value problem (IVP) for the scaling supercritical regularity regime− 1 10< s< 0 in probabilistic
manner. One of the main ingredient is to establish the probabilistic bilinear Strichartz
estimate.
5= 0 on the real line, which is L 2-critical. We prove the local well-posedness of the initial
value problem (IVP) for the scaling supercritical regularity regime− 1 10< s< 0 in probabilistic
manner. One of the main ingredient is to establish the probabilistic bilinear Strichartz
estimate.
We consider the Cauchy problem of the nonlinear Schrödinger equation i∂ t u+∂ x 2 u±u 5= 0 on the real line, which is L 2-critical. We prove the local well-posedness of the initial value problem (IVP) for the scaling supercritical regularity regime− 1 10< s< 0 in probabilistic manner. One of the main ingredient is to establish the probabilistic bilinear Strichartz estimate.
Elsevier
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