11.30 AM, Lecture Hall 2
Conservative regularization compressible flows
Chennai Mathematical Institute.
Quantum theory regularizes some singularities in classical treatments of atomic systems. Similarly, 3D ideal fluid flow 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, we describe a minimal conservative `twirl' regularization of 3D compressible flow, a 3D analogue of KdV. It involves a regularizing length that is like a position-dependent mean free path. Several interesting features of the twirl regularized flow equations are discussed, including conservation laws, a Hamiltonian and Poisson bracket formulation, a priori bounds on norms of velocity and vorticity as well as an application to modeling steady columnar vortices.
This talk is based on joint work with S. Sachdev and A. Thyagaraja.