论文标题
非线性schr {Ö} dinger方程，带有分数噪声
A nonlinear Schr{ö}dinger equation with fractional noise
论文作者
论文摘要
我们研究具有二次非线性和时空分数扰动的随机schr {Ö} dinger方程，在空间维度小于3中。当赫斯特索引足够大时，我们使用经典参数证明了局部问题的局部问题。但是，对于一个小的赫斯特指数，即使对等式的解释也需要一些小心。在这种情况下，必须制定重新归一化的过程，从而导致对模型的灯具解释。然后，我们的定点参数涉及schr {Ö} dinger组的某些特定正则化属性，这使我们能够应对溶液的强不规则性。
We study a stochastic Schr{ö}dinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension less than 3. When the Hurst index is large enough, we prove local well-posedness of the problem using classical arguments. However, for a small Hurst index, even the interpretation of the equation needs some care. In this case, a renormalization procedure must come into the picture, leading to a Wick-type interpretation of the model. Our fixed-point argument then involves some specific regularization properties of the Schr{ö}dinger group, which allows us to cope with the strong irregularity of the solution.
