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On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai
On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai
Mathematical Sciences Undergraduate Honors Theses
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 …