1Bahouri, H., Chemin, J.-Y. and Danchin, R.. Fourier Analysis and Nonlinear Partial Differential Equations, In Grundlehren der Mathematischen Wissenschaften, vol. 343 (Heidelberg: Springer, 2011.
2Beale, J. T., Kato, T. and Majda, A.. Remarks on breakdown of smooth solutions for the 3D Euler equations. Comm. Math. Phys. 94 (1984), 61–66.
3Bejaoui, O. and Majdoub, M.. Global weak solutions for some Oldroyd models. J. Differ. Equ. 254 (2013), 660–685.
4Brezis, H. and Gallouet, T.. Nonlinear Schrödinger evolution equations. Nonlinear Anal. 4 (1980), 677–681.
5Brezis, H. and Wainger, S.. A note on limiting cases of Sobolev embedding and convolution inequalities. Comm. Partial Differ. Equ. 5 (1980), 773–789.
6Chemin, J.-Y. and Masmoudi, N.. About lifespan of regular solutions of equations related to viscoelastic fluids. SIAM J. Math. Anal. 33 (2001), 84–112.
7Chen, Q. and Miao, C.. Global well-posedness of viscoelastic fluids of Oldroyd type in Besov spaces. NonlinearAnal. 68 (2008), 1928–1939.
8Chen, Y. and Zhang, P.. The global existence of small solutions to the incompressible viscoelastic fluid system in 2 and 3 space dimensions. Comm. Partial Differ. Equ. 31 (2006), 1793–1810.
9Constantin, P.. Euler equations, Navier–Stokes equations and turbulence, In Mathematical foundation of turbulent viscous flows, Lecture Notes in Math., vol. 1871,pp. 1–43 (Berlin: Springer, 2006).
10Constantin, P. and Kliegl, M.. Note on global regularity for two-dimensional Oldroyd-B fluids with diffusive stress. Arch. Ration. Mech. Anal 206 (2012), 725–740.
11Constantin, P. and Sun, W.. Remarks on Oldroyd-B and related complex fluid models. Commun. Math. Sci. 10 (2012), 33–73.
12Constantin, P. and Vicol, V.. Nonlinear maximum principles for dissipative linear nonlocal operators and applications. Geom. Funct. Anal. 22 (2012), 1289–1321.
13Elgindi, T. and Rousset, F.. Global regularity for some Oldroyd-B type models. Comm. Pure Appl. Math. 68 (2015), 2005–2021.
14Fang, D. and Zi, R.. Global solutions to the Oldroyd-B model with a class of large initial data. SIAM J. Math. Anal. 48 (2016), 1054–1084.
15Fang, D., Hieber, M. and Zi, R.. Global existence results for Oldroyd-B fluids in exterior domains: the case of non-small coupling parameters. Math. Ann. 357 (2013), 687–709.
16Fernández-Cara, E., Guillén, F. and Ortega, R.. Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind, Handbook of numerical analysis, vol. 8,pp. 543–661 (NorthHolland, Amsterdam: Elsevier, 2002).
17Guillopé, C. and Saut, J.-C.. Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal. 15 (1990), 849–869.
18Guillopé, C. and Saut, J.-C.. Global existence and one-dimensional nonlinear stability of shearingmotions of viscoelastic fluids of Oldroyd type. RAIROModél. Math. Anal. Numér. 24 (1990), 369–401.
19Hieber, M., Naito, Y. and Shibata, Y.. Global existence results for Oldroyd-B fluids in exterior domains. J. Differ. Equ. 252 (2012), 2617–2629.
20Hmidi, T., Keraani, S. and Rousset, F.. Global well-posedness for a Boussinesq-Navier-Stokes system with critical dissipation. J. Differ. Equ. 249 (2010), 2147–2174.
21Hmidi, T., Keraani, S. and Rousset, F.. Global well-posedness for Euler-Boussinesq system with critical dissipation. Comm. Partial Differ. Equ. 36 (2011), 420–445.
22Hu, D. and Lelièvre, T.. New entropy estimates for Oldroyd-B and related models. Commun. Math. Sci. 5 (2007), 909–916.
23Hu, X. and Wang, D.. Local strong solution to the compressible viscoelastic flow with large data. J. Differ. Equ. 249 (2010), 1179–1198.
24Hu, X. and Wang, D.. Global existence for the multi-dimensional compressible viscoelastic flows. J. Differ. Equ. 250 (2011), 1200–1231.
25Karageorghis, A. and Fairweather, G.. The method of fundamental solutions for the numerical solution of the biharmonic equation. J. Comput. Phys. 69 (1987), 434–459.
26Kato, T. and Ponce, G.. Commutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math. 41 (1988), 891–907.
27Kenig, C., Ponce, G. and Vega, L.. Well-posedness of the initial value problem for the Korteweg-de-Vries equation. J. Amer. Math. Soc. 4 (1991), 323–347.
28Lei, Z.. On 2D viscoelasticity with small strain. Arch. Ration. Mech. Anal. 198 (2010), 13–37.
29Lei, Z. and Zhou, Y.. Global existence of classical solutions for the two-dimensional Oldroyd model via the incompressible limit. SIAM J. Math. Anal. 37 (2005), 797–814.
30Lei, Z., Liu, C. and Zhou, Y.. Global solutions for incompressible viscoelastic fluids. Arch. Ration. Mech. Anal 188 (2008), 371–398.
31Lei, Z., Masmoudi, N. and Zhou, Y.. Remarks on the blowup criteria for Oldroyd models. J. Differ. Equ. 248 (2010), 328–341.
32Lemarié-Rieusset, P. G.. Recent developments in the Navier-Stokes problem, Chapman Hall/CRC Research Notes in Mathematics,vol. 431 (Boca Raton, FL: Chapman Hall/CRC, 2002).
33Lin, F., Liu, C. and Zhang, P.. On hydrodynamics of viscoelastic fluids. Comm. Pure Appl. Math. 58 (2005), 1437–1471.
34Lions, P. and Masmoudi, N.. Global solutions for some Oldroyd models of non-Newtonian flows. Chinese Ann. Math. Ser. B 21 (2000), 131–146.
35Masmoudi, N.. Global existence of weak solutions to macroscopic models of polymeric flows. J. Math. Pures Appl. 96 (2011), 502–520.
36Oldroyd, J. G.. Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids. Proc. Roy. Soc. London Ser. A 245 (1958), 278–297.
38Ye, Z. and Xu, X.. Global regularity for the 2D Oldroyd-B model in the corotational case. Math. Methods Appl. Sci. 39 (2016), 3866–3879.
39Zi, R.. Global solution to the incompressible Oldroyd-B model in hybrid Besov spaces. Filomat 30 (2016), 3627–3639.
40Zi, R., Fang, D. and Zhang, T.. Global solution to the incompressible Oldroyd-B model in the critical L p framework: the case of the non-small coupling parameter. Arch. Rational Mech. Anal. 213 (2014), 651–687.