This paper investigates the local-in-time existence and uniqueness of strong solutions in H^s for s >n/2 to the incompressible Oldroyd model equations in R^n, n = 2, 3.The result reads: if u_0, F_0∈ H^s(R^n) with ...This paper investigates the local-in-time existence and uniqueness of strong solutions in H^s for s >n/2 to the incompressible Oldroyd model equations in R^n, n = 2, 3.The result reads: if u_0, F_0∈ H^s(R^n) with s >n/2, then there exists a unique strong solution u, F ∈ C([0, T]; H^s(R^n)), where T = T(‖u_0‖_H^s, ‖F_0‖_H^s) is the local existence time.展开更多
The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global we...The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.展开更多
In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using d...In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.展开更多
The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relation...The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relationship between extensional viscosity and strain rates. The results obtained qualitatively agree with the experimental results. The study makes it practicable to simulate the rheologic behaviors of spinning flow of liquid crystalline polymer using co-rotational Oldroyd fluid B model.展开更多
This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit,...This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.展开更多
In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ...In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data are sufficiently small.展开更多
基金Supported by the National Natural Science Foundation of China(11471103)
文摘This paper investigates the local-in-time existence and uniqueness of strong solutions in H^s for s >n/2 to the incompressible Oldroyd model equations in R^n, n = 2, 3.The result reads: if u_0, F_0∈ H^s(R^n) with s >n/2, then there exists a unique strong solution u, F ∈ C([0, T]; H^s(R^n)), where T = T(‖u_0‖_H^s, ‖F_0‖_H^s) is the local existence time.
文摘The authors consider here some Oldroyd models of non-Newtonian flows consisting of a strong coupling between incompressible Navier-Stokes equations and some transport equations. It is proved that there exist global weak solutions for general initial conditions. The existence proof relies upon showing the propagation in time of the compactness of solutions.
基金supported by The project supported by the Natural Science Foundation of Shandong Province of China (Y2007A06)
文摘In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.
文摘The relationship between the extensional viscosity and material parameters was studied through the analytical formulas of stress and extensional viscosity. The differential equations were solved to obtain the relationship between extensional viscosity and strain rates. The results obtained qualitatively agree with the experimental results. The study makes it practicable to simulate the rheologic behaviors of spinning flow of liquid crystalline polymer using co-rotational Oldroyd fluid B model.
文摘This paper studies the existence and uniqueness of local strong solutions to an Oldroyd-B model with density-dependent viscosity in a bounded domain Ω ⊂ R<sup>d</sup>, d = 2 or 3 via incompressible limit, in which the initial data is “well-prepared” and the velocity field enjoys the slip boundary conditions. The main idea is to derive the uniform energy estimates for nonlinear systems and corresponding incompressible limit.
基金Project supported by the National Natural Science Foundation of China (No. 10225102)the 973 Project of the Ministry of Science and Technology of China and the Doctoral Program Foundation of the Ministry of Education of China.
文摘In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data are sufficiently small.
