Uddhaba Raj Pandey, Ph.D.
Instructor
- Milwaukee WI UNITED STATES
Dr. Uddhaba Pandey is an instructor in the Mathematics Department at MSOE.
Education, Licensure and Certification
Ph.D.
Applied Mathematics
Oklahoma State University
2022
M.S.
Applied Mathematics
Oklahoma State University
2016
M.S.
Mathematics
Tribhuvan University
2009
B.S.
Mathematics
Tribhuvan University
2006
Biography
Areas of Expertise
Affiliations
- American Mathematics Society
- Mathematics Association of America
- Nepal Mathematical Society
- America Nepal Mathematics Association
Languages
- English
- Nepali
- Hindi
Social
Event and Speaking Appearances
2D Anisotropic Boussinesq Equations
(2022) Missouri University of Science and Technlogy Seminar
Nonlinear Decay Rate of the 2D Anisotropic Boussinesq Equation
(2021) OSU Applied Mathmatics Seminar
The Stabilizing Effect of the Temperature on Byuoyancy-Driven Fluids
(2021) 82nd Annual Meeting of the Oklahoma-Arkansas Section Virutal
The Stabilizing Effect of the Temperature on Byuoyancy-Driven Fluids
(2021) 46th New York Regional Garduate Mathematics Conference
The Stabilizing of 3D Rotating Boussinesq Equation with Horizontal Dissipation
(2021) OSU Applied Mathmatics Seminar
Selected Publications
Stability and large-time behavior for the 2D Boussineq system with horizontal dissipation and vertical thermal diffusion
Nonlinear Differential Equations and Applications (NoDEA)2022
This paper solves the stability and large-time behavior problem on perturbations near the hydrostatic equilibrium of the two-dimensional Boussinesq system with horizontal dissipation and vertical thermal diffusion. The spatial domain \(\Omega \) is \({\mathbb {T}} \times {\mathbb {R}}\) with \({\mathbb {T}}=[0,1]\) being the 1D periodic box and \({\mathbb {R}}\) being the whole line. The results presented in this paper establish the observed stabilizing phenomenon and stratifying patterns of the buoyancy-driven fluids as mathematically rigorous facts. The stability and large-time behavior problem concerned here is difficult due to the lack of the vertical dissipation and horizontal thermal diffusion. To make up for the missing regularization, we exploit the smoothing and stabilizing effect due to the coupling and interaction between the temperature and the fluids. By constructing suitable energy functional and introducing the orthogonal decomposition of the velocity and the temperature into their horizontal averages and oscillation parts, we are able to establish the stability in the Sobolev space \(H^2\) and obtain algebraic decay rates for the oscillation parts in the \(H^1\)-norm.
The stabilizing effect of the temperature on buoyancy-driven fluids
Indiana University Mathematics Journal2020
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on perturbations near the hydrostatic balance. This problem can be extremely difficult when the system lacks full dissipation. This paper solves the stability problem for a two-dimensional Boussinesq system with only vertical dissipation and horizontal thermal diffusion. We establish the stability for the nonlinear system and derive precise large-time behavior for the linearized system. The results presented in this paper reveal a remarkable phenomenon for buoyancy driven fluids. That is, the temperature actually smooths and stabilizes the fluids. If the temperature were not present, the fluid is governed by the 2D Navier-Stokes with only vertical dissipation and its stability remains open. It is the coupling and interaction between the temperature and the velocity in the Boussinesq system that makes the stability problem studied here possible. Mathematically the system can be reduced to degenerate and damped wave equations that fuel the stabilization.
