6 papers
Curl Measure Fields, the Generalized Stokes Theorem and Vorticity Fluxes
Gui-Qiang G. Chen, Franz Gmeineder, Monica Torres
We introduce and analyze the class of curl-measure fields that are -integrable vector fields whose distributional curl is a vector-valued finite Radon measure…
Extended Divergence-Measure Fields, the Gauss-Green Formula, and Cauchy Fluxes
Gui-Qiang G. Chen, Christopher Irving, Monica Torres
We establish the Gauss-Green formula for extended divergence-measure fields (i.e., vector-valued measures whose distributional divergences are Radon measures) over open sets. We pr…
A Principle of Maximum Entropy for the Navier-Stokes Equations
Gui-Qiang G. Chen, James Glimm, Hamid Said
A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of d…
Vanishing Mach Number Limit of Stochastic Compressible Flows
Gui-Qiang G. Chen, Michele Coti Zelati, Chin Ching Yeung
We study the vanishing Mach number limit for the stochastic Navier-Stokes equations with -type pressure laws, with focus on the one-dimensional case. We prove that, if the stoch…
Morawetz's Contributions to the Mathematical Theory of Transonic Flows, Shock Waves, and Partial Differential Equations of Mixed Type
Gui-Qiang G. Chen
This article is a survey of Cathleen Morawetz's contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed elliptic-hyper…
Gas Dynamics Equations: Computation
Gui-Qiang G. Chen
Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosio…