Bio
Terry Moschandreou is a researcher affiliated with the University of Western Ontario and the Thames Valley District School Board in Canada. He holds a Doctor of Philosophy in Applied Mathematics from Western Ontario. His research interests span a wide range of fields including Applied Mathematics, Biomechanical Engineering, Computer Aided Engineering, Biochemical Engineering, Fluid Flow and Transfer Processes, Computational Fluid Dynamics (CFD), Dynamical Systems, and Nonlinear Dynamics. Dr. Moschandreou has authored works such as 'Exploring Finite-Time Singularities and Onsager’s Conjecture with Endpoint Regularity in the Periodic Navier Stokes Equations' and 'Pulmonary Alveolar Microlithiasis, Case Report', demonstrating a diverse research portfolio that bridges theoretical mathematics and practical engineering applications.
Educational Journey
Western Ontario and Thames Valley District School Board
Doctor of Philosophy Applied Mathematics
Experience
Western Ontario and Thames Valley District School Board
0 - 0Research
Exploring Finite-Time Singularities and Onsager’s Conjecture with Endpoint Regularity in the Periodic Navier Stokes Equations
It has recently been proposed by the author of the present work that the periodic NS equations (PNS) with high energy assumption can breakdown in finite time but with sufficient low energy scaling the equations may not exhibit finite time blowup. This article gives a general model using specific periodic special functions, that is degenerate elliptic Weierstrass P functions whose presence in the governing equations through the forcing terms simplify the PNS equations at the centers of cells of the 3-Torus. Satisfying a divergence free vector field and periodic boundary conditions respectively with a general spatio-temporal forcing term f which is smooth and spatially periodic, the existence of solutions which blowup in finite time for PNS can occur starting with the first derivative and higher with respect to time. P. Isett (2016) has shown that the conservation of energy fails for the 3D incompressible Euler flows with Ho ̈lder regularity below 1/3. (Onsager’s second conjecture) The endpoint regularity in Onsager’s conjecture is addressed, and it is found that conservation of energy occurs when the Ho ̈lder regularity is exactly 1/3. The endpoint regularity problem has important connections with turbulence theory. Finally very recent developed new governing equations of fluid mechanics are proposed to have no finite time singularities.
