Date of Graduation
8-2024
Document Type
Thesis
Degree Name
Bachelor of Science in Mathematics
Degree Level
Undergraduate
Department
Mathematical Sciences
Advisor/Mentor
Bradshaw, Zachary
Committee Member/Reader
Clay, Matt
Committee Member/Second Reader
Hoyer, Jennifer
Committee Member/Third Reader
Levine, Bill
Abstract
In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over recent results and discuss the outlook mathematicians have today on solving the Millennium Problem.
Citation
Prabhudesai, A. (2024). On Weak Solutions and the Navier-Stokes Equations. Mathematical Sciences Undergraduate Honors Theses Retrieved from https://scholarworks.uark.edu/mascuht/8