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arXiv · 1804.07894

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

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.

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Joonhyun La. 2018-04-21. Decay of solutions of diffusive Oldroyd-B system in $\mathbb{R}^2$. https://arxiv.org/abs/1804.07894

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