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Mathematics > Analysis of PDEs

arXiv:1804.07894 (math)
[Submitted on 21 Apr 2018 (v1), last revised 24 Apr 2018 (this version, v2)]

Title:Decay of solutions of diffusive Oldroyd-B system in $\mathbb{R}^2$

Authors:Joonhyun La
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Abstract:We show that strong solutions of 2D diffusive Oldroyd-B systems in $\mathbb{R}^2$ decay at an algebraic rate, for a large class of initial data. The main ingredient for the proof is the following fact; an Oldroyd-B system is a macroscopic closure of a Fokker-Planck-Navier-Stokes system, and the free energy of this Fokker-Planck-Navier-Stokes system decays over time. In particular, $\norm{u}_{L^\infty_t L^2_x}$ and $\norm{\nabla_x u}_{L^2_t L^2_x }$ are uniformly bounded for all time.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.07894 [math.AP]
  (or arXiv:1804.07894v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.07894

Submission history

From: Joonhyun La [view email]
[v1] Sat, 21 Apr 2018 05:25:58 UTC (11 KB)
[v2] Tue, 24 Apr 2018 18:44:24 UTC (11 KB)
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