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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer Berlin Heidelberg

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DOI

10.1007/s00205-016-1072-1

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1432-0673

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The Liouville Theorem and the Emphasis Type="Ital

Authors: Wei Luo Zhaoyang Yin
Publish Date: 2016/12/29
Volume: 224, Issue: 1, Pages: 209-231
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Abstract

In this paper we mainly study the finite extensible nonlinear elastic FENE dumbbell model with dimension d geqq 2 in the whole space We first prove that there is only the trivial solution for the steadystate FENE model under some integrable condition The obtained results generalize and cover the classical results for the stationary Navier–Stokes equations We then obtain that the L 2 decay rate of the velocity of the corotation FENE model is 1+tfracd4 when d geqq 3 and lnke+t kin mathbbN+ when d = 2 This result improves considerably the recent result of Schonbek SIAM J Math Anal 41564–587 2009 Moreover we investigate the L 2 decay of solutions to the general FENE model

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Other Papers In This Journal:
  1. Optimal Design in Conductivity Under Locally Constrained Heat Flux
  2. Regularity Issues in the Problem of Fluid Structure Interaction
  3. Negative Eigenvalues of Two-Dimensional Schrödinger Operators
  4. Dobrushin States in the $${\phi^4_1}$$ Model
  5. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  6. Counterexamples to the Sonic Criterion
  7. Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution
  8. On Nonlinear Stochastic Balance Laws
  9. Weak Solutions of the Navier–Stokes Equations for Compressible Flows in a Half-Space with No-Slip Boundary Conditions
  10. Generalized Transition Fronts for One-Dimensional Almost Periodic Fisher-KPP Equations
  11. The Gel’fand Problem for the Biharmonic Operator
  12. The Existence Problem for Steiner Networks in Strictly Convex Domains
  13. Stability of Detonation Profiles in the ZND Limit
  14. Uniqueness of Absolute Minimizers for $${L^\infty}$$-Functionals Involving Hamiltonians $${H(x,p)}$$H(x,p)
  15. A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear Elastic Energy in Two Dimensions
  16. Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary
  17. The Toda System and Clustering Interfaces in the Allen–Cahn equation
  18. A Stability Criterion for Two-Fluid Interfaces and Applications
  19. Long-Time Convergence of an Adaptive Biasing Force Method: The Bi-Channel Case
  20. Displacement Convexity and Minimal Fronts at Phase Boundaries
  21. Gradient Bounds for Elliptic Problems Singular at the Boundary
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