کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5024388 | 1470390 | 2018 | 34 صفحه PDF | دانلود رایگان |
We explore the existence of global weak solutions to the Hookean dumbbell model, a system of nonlinear partial differential equations that arises from the kinetic theory of dilute polymers, involving the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions, coupled to a Fokker-Planck-type parabolic equation. We prove the existence of large-data global weak solutions in the case of two space dimensions. Indirectly, our proof also rigorously demonstrates that, in two space dimensions at least, the Oldroyd-B model is the macroscopic closure of the Hookean dumbbell model. In three space dimensions, we prove the existence of large-data global weak subsolutions to the model, which are weak solutions with a defect measure, where the defect measure appearing in the Navier-Stokes momentum equation is the divergence of a symmetric positive semidefinite matrix-valued Radon measure.
Journal: Nonlinear Analysis: Real World Applications - Volume 39, February 2018, Pages 362-395