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ON THE LOCAL WELL-POSEDNESS FOR THE DUMBBELL MODEL OF polymeric fluids

Journal of Partial Differential Equations 2008年第3期21卷 234-252页

作者： Zhang Ping Zhang Zhifei Academy of Mathematics & Systems Science CAS Beijing 100080 China School of Mathematical Science Peking University Beijing 100871 China

In this paper, we consider the local well-posedness of smooth solutions to a coupled microscopic-macroscopic model for polymeric fluid in general space dimension and with general initial data in Holder space.

关键词： polymeric fluids Navier-Stokes equations Littlewood-Paley decom-sposition.

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Enhanced Constitutive Theories for Classical Thermoviscoelastic polymeric fluids

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Applied Mathematics 2022年第11期13卷 917-947页

作者： Karan S. Surana Thomas J. Ezell Department of Mechanical Engineering University of Kansas Lawrence KS USA

This paper presents ordered rate nonlinear constitutive theories for thermoviscoelastic fluids based on Classical Continuum Mechanics (CCM). We refer to these fluids as classical thermoviscoelastic polymeric fluids. The conservation and balance laws of CCM constitute the core of the mathematical model. Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The constitutive theories for the Cauchy stress tensor consider convected time derivatives of Green’s strain tensor or the Almansi strain tensor up to order n and the convected time derivatives of the Cauchy stress tensor up to order m. The resulting constitutive theories of order (m, n) are based on integrity and are valid for dilute as well as dense polymeric, compressible, and incompressible fluids with variable material coefficients. It is shown that Maxwell, Oldroyd-B, and Giesekus constitutive models can be described by a single constitutive theory. It is well established that the currently used Maxwell and Oldroyd-B models predict zero normal stress perpendicular to the flow direction. It is shown that this deficiency is a consequence of not retaining certain generators and invariants from the integrity (complete basis) in the constitutive theory and can be corrected by including additional generators and invariants in the constitutive theory. Similar improvements are also suggested for the Giesekus constitutive model. Model problem studies are presented for BVPs consisting of fully developed flow between parallel plates and lid-driven cavities utilizing the new constitutive theories for Maxwell, Oldroyd-B, and Giesekus fluids. Results are compared with those obtained from using currently used constitutive theories for the three polymeric fluids.

关键词： polymeric fluids Maxwell Oldroyd-B Giesekus Mathematical Models Nonlinear Rate Constitutive Theories Representation Theorem Integrity Generators Invariants

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