带有分数阶耗散的三维广义Oldroyd-B模型的整体正则性

Abstract

CLC Number:

O175.29

Qiuyue Zhang. Global Regularity for 3D Generalized Oldroyd-B Type Models with Fractional Dissipation[J].Acta mathematica scientia,Series A, 2019, 39(5): 1125-1135.

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References 30

1	Oldroyd J G . Non-Newtonian effects in steady motion of some idealized elastico-viscous liqids. Proc Roy Soc Lond Ser A, 1958, 245: 278- 297 doi: 10.1098/rspa.1958.0083
2	Bird R B , Curtiss C F , Armstrong R C , Hassager O . Dynamics of Polymeric Liquids, Vol 1:Fluid Mechanics. 2nd ed New York: Wiley, 1987
3	Lin F , Liu C , Zhang P . On hydrodynamics of viscoelastic fluids. Comm Pure Appl Math, 2005, 51: 1437- 1471
4	Guillopé C , Saut J C . Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal, 1990, 15: 849- 869 doi: 10.1016/0362-546X(90)90097-Z
5	Guillopé C , Saut J C . Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroy type. RAIROMod él Math Anal Num ér, 1990, 24: 369- 401 doi: 10.1051/m2an/1990240303691
6	Chemin J Y , Masmoudi N . About lifespan of regular solutions of equations related to viscoelastic fluids. SIAM J Math Anal, 2006, 33: 84- 112
7	Chen Q , Miao C . Global well-posedness of viscoelastic fluids of Oldroyd type in Besov spaces. Nonlinear Anal, 2008, 68: 1928- 1939 doi: 10.1016/j.na.2007.01.042
8	Constantin P , Sun W . Remarks on Oldroyd-B and related complex fluid models. Commun Math Sci, 2012, 10: 33- 73 doi: 10.4310/CMS.2012.v10.n1.a3
9	Fang D , Hieber M , Zi R . Global existence results for Oldroyd-B fluids in exterior domains:the case of non-small coupling parameters. Math Ann, 2013, 357: 687- 709 doi: 10.1007/s00208-013-0914-5
10	Fang D , Zi R . Global solutions to the Oldroyd-B model with a class of large initial data. SIAM J Math Anal, 2016, 48: 1054- 1084 doi: 10.1137/15M1037020
11	Hieber M , Naito Y , Shibata Y . Global existence results for Oldroyd-B fluids in exterior domains. J Differ Equ, 2012, 252: 2617- 2629 doi: 10.1016/j.jde.2011.09.001
12	Lei Z . On 2D viscoelasticity with small strain. Arch Ration Mech Anal, 2010, 198: 13- 37 doi: 10.1007/s00205-010-0346-2
13	Lei Z , Liu C , Zhou Y . Global existence for a 2D incompressible viscoelastic model with small strain. Commun Math Sci, 2007, 5: 595- 616 doi: 10.4310/CMS.2007.v5.n3.a5
14	Zi R , Fang D , Zhang T . Global solution to the incompressible Oldroyd-B model in the critical L^p framework:the case of the non-small coupling parameters. Arch Ration Mech Anal, 2014, 213: 651- 687 doi: 10.1007/s00205-014-0732-2
15	Lions P L , Masmoudi N . Global solutions for some Oldroyd models of non-Newtonian flows. Chinese Ann Math Ser B, 2000, 21: 131- 146 doi: 10.1142/S0252959900000170
16	Elgndi T M , Rousset F . Global regularity for some Oldroyd type models. Comm Pure Appl Math, 2015, 68 (11): 2005- 2021 doi: 10.1002/cpa.21563
17	Elgndi T M , Liu J . Global wellposedness to the generalized Oldroyd type models in ${{\mathbb{R}}^3}$. J Diffrential Equations, 2015, 259: 1958- 1966 doi: 10.1016/j.jde.2015.03.026
18	Constantin P , Kliegl M . Note on global regularity for two-dimensional Oldroyd-B fluids with diffusive stress. Arch Ration Mech Anal, 2012, 206: 725- 740 doi: 10.1007/s00205-012-0537-0
19	Masmoudi N . Global existence of weak solutions to the FENE dumbbell model of polymeric flows. Invent Math, 2013, 191: 427- 500 doi: 10.1007/s00222-012-0399-y
20	Qian J . Well-posedness in critical spaces for incompressible viscoelastic fluid system. Nonlinear Anal, 2010, 72: 3222- 3234 doi: 10.1016/j.na.2009.12.022
21	Sun Y , Zhang Z . Global well-posedness for the 2D micro-macro models in the bounded domain. Comm Math Phys, 2011, 303: 361- 383 doi: 10.1007/s00220-010-1170-0
22	Zhang T, Fang D. Global well-posedness for the incompressible viscoelastic fluids in the critical L^p framework. 2011, arXiv: 1101.5864v2[math.AP]
23	Wu J . Generalized MHD equations. J Differential Equations, 2003, 195: 284- 312 doi: 10.1016/j.jde.2003.07.007
24	Wan R . Global regularity for generalized Hall magneto-hydrodynamics systems. Electron J Differential Equations, 2015, 179: 1- 18
25	Wan R. Global well-posedness to the subcritical Oldroyd-B type models in 2D. 2015, arXiv: 1509.07663v2[math.AP]
26	Yang W , Jiu Q , Wu J . The 3D incompressible magnetohydrodynamic equations with fractional partial dissipation. J Differential Equations, 2019, 266 (1): 630- 652 doi: 10.1016/j.jde.2018.07.046
27	Kato T , Ponce G . Commutator estimates and the Euler and Navier-Stokes equations. Commun Pure Appl Math, 1988, 41: 891- 907 doi: 10.1002/cpa.3160410704
28	Majda A J , Bertozzi A L . Vorticity and Incopressible Flow. Cambrige: Cambrige University Press, 2001
29	Bony J M . Calcul symbolique et propagation des sigularites pour les equations aux derivees partielles non lineaires. Ann Sci Ecole Norm Sup, 1981, 14: 209- 246 doi: 10.24033/asens.1404
30	Chemin J Y . Perfect Incompressible Fluids. New York: Clarendon Press, 1998

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Global Regularity for 3D Generalized Oldroyd-B Type Models with Fractional Dissipation

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