ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 35, 60, 76 He, Xinyu, University of Warwick, England A probabilistic method for vortex motion in turbulent fluids Consider a Navier-Stokes incompressible turbulent fluid in two spatial dimensions. Assume a vortex in the fluid possesses a continuous trajectory, x(t), described by a stochastic differential equation. Based on [N], we derive the evolution equation of ψ(x, t), the probability of finding the vortex in position x at time t. In contrast to stochastic mechanics, the velocity of the vortex intrinsically has both gradient and rotational parts, hence ψ is in general multi-valued. We present some solutions of the evolution equation in this context. References: [H] X. He, Chaos, Solitons and Fractals 4 (1994), 693-699. [N] E. Nelson, Lecture Notes in Mathematics 1362 (1988), 428-450.