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Brownian Motion of A Particle Immersed in a Viscous, Incompressible, Thermally Fluctuating Solvent
Xiong, Wei

2008, Doctor of Philosophy, Ohio State University, Mathematics.

My current work concerns the hydrodynamics of particles immersed in a thermally fluctuating, viscous, incompressible solvent. The governing equations stipulate conservation of momentum in the fluid, conservation of linear and angular momentum of the particle, and no-slip boundary conditions on the boundary of the particle. Is there existence and uniqueness for the solution? What are the limit theorems when time goes to infinity? These problems not only provide more detailed study of physical Brownian motions but also give a testing ground for the techniques in stochastic partial differential equations.

This thesis is a first step to answer these questions. We analyze parts of the system: stochastic Stokes equations in the whole space, passive point particle, passive particle with finite size. We characterize the regularity properties and statistical behaviors of the solution $u(t,x)$ and $p(t,x)$ to the stochastic Stokes equations in the whole space. We give existence and uniqueness results for passive particles (a point particles as well as a finite size particle), and we give limit theorems for a point particle when the time goes to infinity.


Peter March, PhD (Advisor)
Avner Friedman, PhD (Committee Member)
Saleh Tanveer, PhD (Committee Member)

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Xiong, W. (2008). Brownian Motion of A Particle Immersed in a Viscous, Incompressible, Thermally Fluctuating Solvent. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Xiong, Wei. "Brownian Motion of A Particle Immersed in a Viscous, Incompressible, Thermally Fluctuating Solvent." Electronic Thesis or Dissertation. Ohio State University, 2008. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Xiong, Wei "Brownian Motion of A Particle Immersed in a Viscous, Incompressible, Thermally Fluctuating Solvent." Electronic Thesis or Dissertation. Ohio State University, 2008. https://etd.ohiolink.edu/

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