Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.

The Duchamp Research Portal: Moving an Idea to Proof of Concept

Presentation from the MARAC conference in Pittsburgh, PA on April 14–16, 2016. S15 - The Duchamp Research Portal: Moving an Idea to Proof of Concept.

Program for the Fall 2015 MARAC Meeting: Moving Mountains: Ingenuity and Innovation in Archives

The program for the Fall 2015 MARAC meeting, "Moving Mountains: Ingenuity and Innovation in Archives" held October 8-10 in Roanoke, Virginia.