Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows
Related Research Unit(s)
|Journal / Publication||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - Aug 2015|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-84923776621&origin=recordpage|
We consider the Cauchy problem for incompressible viscoelastic uids in the whole space Rd (d = 2, 3). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of global smooth solutions near equilibrium. Then under additional assumptions that the initial data belong to L1 and their Fourier modes do not degenerate at low frequencies, we obtain the optimal L2 decay rates for the global smooth solutions and their spatial derivatives. At last, we establish the weak-strong uniqueness property in the class of finite energy weak solutions for the incompressible viscoelastic system.
- Long-time behavior, Navier-Stokes equations, Optimal decay rate, Viscoelastic flow, Weak-strong uniqueness
Discrete and Continuous Dynamical Systems- Series A, Vol. 35, No. 8, 08.2015, p. 3437-3461.
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Hu, X & Wu, H 2015, 'Long-time behavior and weak-strong uniqueness for incompressible viscoelastic flows', Discrete and Continuous Dynamical Systems- Series A, vol. 35, no. 8, pp. 3437-3461. https://doi.org/10.3934/dcds.2015.35.3437