环面上随机2D流体模型的异常正则化和弱唯一性
We consider stochastic 2D Euler equations with L2 initial data on the torus, driven by Kraichnan transport noise with parameter α ∈ (0, 1/2). Thanks to the noise, the equation admits weak solutions with anomalous regularity, roughly speaking, the H1−α norm of solution is square integrable in time. This enables us to prove the anomalous dissipation and uniqueness in law of weak solutions through Girsanov transform. Similar results hold for stochastic 2D mSQG equations with suitably chosen parameters. The talk is based on a joint work with Dejun Luo.
我们考虑环面上由参数为α ∈ (0，1/2)的Kraichnan输运噪声驱动的具有L2初值的随机2D-欧拉方程。由于噪声，该方程允许具有异常正则性的弱解，粗略地说，解的H1α范数在时间上是平方可积的。这使我们能够通过Girsanov变换证明弱解定律的反常耗散性和唯一性。对于具有适当选择的参数的随机2D mSQG方程，类似的结果成立。这个演讲是基于与罗德军的合作。
相关预告推荐
-
1
School Colloquium——Sparse Hypergraphs: from Theory to Applications
时 间：2019-03-29 15:00:00
-
2
Probability Seminar——群上随机游动的常返性、尾$\sigma-$代数和零渐进值域熵
时 间：2018-12-03 10:00:00
-
3
Geometric Analysis and Mathematical Relativity Seminar——Obata’s rigidity theorem on manifold with boundary
时 间：2018-11-23 10:10:00
-
4
Modelling function-valued processes with non-separable and/or non-stationary covariance structure
时 间：2020-12-10 16:00:00
-
5
Probability Seminar——The high dimensional Ising model with free boundary conditions
时 间：2020-12-14 14:00:00
-
6
Analysis and PDE Seminar——Stability of the Couette flow for 2D Navier-Stokes Boussinesq system
时 间：2020-12-15 14:00:00
-
7
Atiyah and Todd classes arising from integrable distributions
时 间：2018-11-20 16:00:00
-
8
Course of Undergraduate Young Talent Project: Topics in Analysis
时 间：2019-03-05 18:00:00
-
9
Analysis and PDE Seminar——Anisotropic Dynamical Horizons Arising in Gravitational Collapse
时 间：2020-12-15 15:00:00
-
10
图像科学中的数学
时 间：2018-11-23 18:30:00
