Navier-Stokes Equations in the Whole Space with an Eddy Viscosity

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Mohammadi, Mehrad | 2022

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 55036 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaraki, Mahmoud
Abstract:
We study the Navier-Stokes equations with an extra Eddy viscosity term in the whole space . We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove that when the regularizing parameter goes to zero, the solution of the regularized system converges to a turbulent solution of the initial system. In the first chapter, we have dedicated the necessary preliminaries and then in the second chapter, we have introduced the types of solutions. The third chapter introduces the necessary tools and their properties, with the help of which in the next chapter we have been able to make estimates and obtain their extensions to prove the key theorem of the study. In the fifth chapter of this research, we have provided the necessary context for the sixth chapter, which is the proof of the result of this research. Finally, we have dedicated the last chapter to additional points and research that can be examined in the future.
Keywords:
Navier-Stokes Equation ; Turbulent Solutions ; Eddy Viscosities