Global Solutions for Incompressible Viscoelastic Fluids
نویسندگان
چکیده
We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data. The results hold in both two and three dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals and mixture problems.
منابع مشابه
On 2D Viscoelasticity with Small Strain
An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, ...
متن کاملGlobal Strong Solution to the Density-dependent Incompressible Viscoelastic Fluids
The existence and uniqueness of the global strong solution with small initial data to the three-dimensional density-dependent incompressible viscoelastic fluids is established. The local existence and uniqueness of the global strong solution with small initial data to the three-dimensional compressible viscoelastic fluids is also obtained. A new method is developed to estimate the solution with...
متن کاملOn Stochastic Models Describing the Motions of Randomly Forced Linear Viscoelastic Fluids
This paper is devoted to the analysis of stochastic equations describing the motions of a large class of incompressible linear viscoelastic fluids in two-dimensional subject to periodic boundary condition and driven by random external forces. To do so we distinguish two cases, and for each case a global existence result of probabilistic weak solution is expounded in this paper. We also prove th...
متن کاملMathematical Results for Some Models of Viscoelastic Fluids
We give a short survey of several results concerning mathematical analysis of models describing flows of incompressible rate type fluids. After recalling the system of governing equations, we first present the result of P.-L. Lions and N. Masmoudi [4] about global existence of solution to a special case of Oldroyd model. Then we present results of F.-H. Lin, C. Liu and P. Zhang [3] and Y. Chen ...
متن کاملNewtonian Limit for Weakly Viscoelastic Fluid Flows of Oldroyd Type
This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in IR or T N for N = 2, 3, when the Weissenberg number (relaxation time measuring the elasticity effect in the fluid) tends to zero. More precisely, we prove that the velocity field an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009