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Signed-Measure Valued Stochastic Partial Differential Equations with Applications in 2D Fluid Dynamics

Seadler, Bradley T.
http://rave.ohiolink.edu/etdc/view?acc_num=case1333062148

Abstract Details

2012, Doctor of Philosophy, Case Western Reserve University, Mathematics.
We note the interesting phenomenon that the Kantorovich-Rubinstein metric is not complete on the space of signed measures. Consequently, we introduce a new metric with a useful partial completeness property. With this metric, a general result about the Hahn-Jordan decomposition of solutions of stochastic partial differential equations is shown. These general results are applied to the smoothed Stochastic Navier-Stokes equations. As an application, we derive that the vorticity of the fluid is conserved for a solution of the Stochastic Navier-Stokes equations.
Dr. Peter Kotelenez, PhD (Committee Chair)
Dr. Elizabeth Meckes, PhD (Committee Member)
Dr. Manfred Denker, PhD (Committee Member)
Dr. Marshall Leitman, PhD (Committee Member)
106 p.
Aerospace Engineering; Mathematics; Physics
Stochastic; Partial; Differential; Equations; Hahn; Jordan; Fluid; Dynamics; 2D

Recommended Citations

Citations

  • Seadler, B. T. (2012). Signed-Measure Valued Stochastic Partial Differential Equations with Applications in 2D Fluid Dynamics [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1333062148

    APA Style (7th edition)

  • Seadler, Bradley. Signed-Measure Valued Stochastic Partial Differential Equations with Applications in 2D Fluid Dynamics. 2012. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1333062148.

    MLA Style (8th edition)

  • Seadler, Bradley. "Signed-Measure Valued Stochastic Partial Differential Equations with Applications in 2D Fluid Dynamics." Doctoral dissertation, Case Western Reserve University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=case1333062148

    Chicago Manual of Style (17th edition)

case1333062148
714
© 2012, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.