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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 12
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Articles

Optimal time decay rate for compressible viscoelastic equations in critical spaces

Junxiong JiaDepartment of Mathematics, Xi’an Jiaotong University, Xi’an, China.;Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS),, Beijing, China.Correspondence[email protected]
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Jigen PengDepartment of Mathematics, Xi’an Jiaotong University, Xi’an, China.;Beijing Center for Mathematics and Information Interdisciplinary Sciences (BCMIIS),, Beijing, China.View further author information
Pages 2044-2064 | Received 13 Mar 2016, Accepted 08 Jun 2016, Published online: 24 Jun 2016

References

  • Lei Z, Liu C, Zhou Y. Global solutions of incompressible viscoelastic fluids. Arch. Rational Mech. Anal. 2008;188:371–398.
  • Lin F, Liu C, Zhang P. On hydrodynamics of viscoelastic fluids. Commun. Pure Appl. Math. 2005;58:1437–1471.
  • Lin F, Zhang P. On the initial-boundary value problem of the incompressible viscolastic fluid system. Commun. Pure Appl. Math. 2008;61:539–558.
  • Zhang T, Fang D. Global existence of strong solution for equations related to the incompressible viscoelastic fluids in the critical Lp framework. SIAM J. Math. Anal. 2013;44:2266–2288.
  • Qian J, Zhang Z. Global well-posedness for compressible viscoelastic fluids near equilibrium. Arch. Rational Mech. Anal. 2010;198:835–868.
  • Hu X, Wang D. Global existence for the multi-dimensional compressible viscoelastic flows. J. Differ. Equ. 2011;250:1200–1231.
  • Lions P, Masmoudi N. Global solutions for some Oldroyd models of non-Newtonian flows. Chin. Ann. Math. Ser. B. 2000;21:131–146.
  • Jia J, Peng J, Mei Z. Well-posedness and time-decay for compressible viscoelastic fluids in critical Besov space. J. Math. Anal. Appl. 2014;418:638–675.
  • Ponce G. Global existence of small solution to a class of nonlinear evolution equations. Nonlinear Anal. 1985;9:339–418.
  • Guo Y, Wang Y. Decay of dissipative equations and negative sobolev spaces. Commun. Partial Differ. Equ. 2012;37:2165–2208.
  • Li H, Zhang T. Large time bahavior of isentropic compressible Navier--Stokes system in ℝ3. Math. Meth. Appl. Sci. 2011;34:670–682.
  • Hoff D, Zumbrun K. Multi-dimensional diffusion waves for the Navier--Stokes equations of compressible flow. Indiana Univ. Math. J. 1995;44:604–676.
  • Hoff D, Zumbrun K. Pointwise decay estimates for multi-dimensional Navier--Stokes diffusion waves. Z. Angew. Math. Phys. 1997;48:597–614.
  • Liu T, Wang W. The pointwise estimates of diffusion waves for the Navier--Stokes equaions in odd multi-dimensions. Commun. Math. Phys. 1998;196:145–173.
  • Li DL. The green’s function of the Navier--Stokes equations for gas dynamics in ℝ3. Commun. Math. Phys. 2005;257:579–619.
  • Okita M. Optimal decay rate for strong solutions in critical spaces to the compressible Navier--Stokes equations. J. Differ. Equ. 2014;257:3850–3867.
  • Hu X, Wu G. Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows. (English summary). SIAM J. Math. Anal. 2013;45:2815–2833.
  • Chemin J-Y, Lerner N. Flot de champs de vecteurs non lipschitziens etéquations de Navier--Stokes [Flow fields of non-Lipschitz vectors and Navier-Stokes equations]. J. Differ. Equ. 1992;121:314–328.
  • Bahouri H, Chemin J, Danchin R. Fourier analysis and nonlinear partial differential equations. Grundlehren der mathematischen Wissenschaften [Basics of mathematical Sciences]. Berlin: Springer-Verlag; 2011.
  • Danchin R. Fourier analysis methods for PDE’s. Lecture notes. 2005. November 14. Available from: http://perso-math.univ-mlv.fr/users/danchin.raphael/cours/courschine.pdf.
  • Chen Q, Miao C, Zhang Z. Global well-posedness for compressible Navier--Stokes equations with highly oscillating initial velocity. Commun. Pure. Appl. Math. 2010;LXIII:1173–1224.
  • Charve F, Danchin R. A gloal existence result for the compressible Navier--Stokes equations in the critical Lpframework. Arch. Ration. Mech. Anal. 2010;198:233–271.
  • Hoff D, Zumbrun K. Mutli-dimensional diffusion waves for the Navier--Stokes equations of compressible flow. Indiana Univ. Math. J. 1995;44:603–676.

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