March 28, 2024

Nonlinear Stability and the Bénard Problem

Fluid motion driven by thermal gradients (Rayleigh-Bénard convection) is a common and important phenomenon in nature. Convection is a major feature of the dynamics in the oceans, the atmosphere, and the interior of stars and Earth. Rayleigh-Bénard convection problems also find numerous industrial applications. In this talk, I will present the application of the energy method to investigate the stability of the zero solution of the diffusion equations. Then, I will propose a mathematical model to study the Rayleigh-Bénard convection configuration for a viscoelastic class of fluid. Linear and nonlinear stability analyses of the problem will be discussed. Additionally, I will present some numerical results.

About the speaker

Dr. B Mahanthesh earned his M.S in mathematics from the Kuvempu University, India, and his Ph.D. in applied mathematics at the same university in 2018. He is currently a post-doctoral fellow at the School of Mathematical and Statistical Sciences, UTRGV, TX. He was an assistant professor at Christ University, Bangalore, India, from 2016 to 2021. His research interests are mathematical modeling, theoretical fluid mechanics, and statistical optimization techniques. He is the author and co-author of numerous research publications in reputed journals.