Title: Anomalous regularization for the nonsmooth Kraichnan and Kazantsev-Kraichnan models on the torus
Abstract: The nonsmooth Kraichnan model is given by a passive scalar (transport) equation, with Gaussian incompressible noise which is white-in-time, isotropic and nonsmooth in space. This model exhibits anomalous dissipation and anomalous regularization. We show that a similar anomalous regularization result holds for a version of the nonsmooth Kraichnan model on the torus, where the isotropy property is lost. We also show a similar result for the nonsmooth Kazantsev-Kraichnan model on the torus. Based on joint ongoing work with Lucio Galeati and Sotirios Kotitsas.