Physics

Dr. Govind Krishnaswami
Chennai Mathematical Institute

Quantum theory regularizes some singularities in classical
treatments of atomic systems. Similarly, 3D ideal fluid equations may
develop shock-like and vortical singularities, not manifested in
physical flows. Navier-Stokes viscosity provides a dissipative
regularization. In 1D we also have a conservative KdV regularization
with wide applications. After motivating the ideas with 1D flows and
briefly surveying the literature on singularities, we describe a new
minimal conservative `twirl' regularization of 3D compressible flow, a
sort of 3D analogue of KdV. The physical interpretation and
mathematical properties of the regularised equations will be
discussed. The extension to magnetohydrodynamics and an attempt to
model steady tornadoes will be outlined if time permits. This talk is
based on joint work with S. Sachdev and A. Thyagaraja.