scholarly journals Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity

2015 ◽  
Vol 54 (4) ◽  
pp. 3789-3828 ◽  
Author(s):  
Michael Winkler
Keyword(s):  
Nonlinear Diffusion ◽  
Stokes System ◽  
Large Time ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Time Behavior

scholarly journals Large time behavior of nonlocal aggregation models with nonlinear diffusion

2008 ◽  
Vol 3 (4) ◽  
pp. 749-785 ◽  
Author(s):  
Martin Burger ◽  
◽  
Marco Di Francesco ◽  
Keyword(s):  
Nonlinear Diffusion ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior

scholarly journals On $ L^1 $ estimates of solutions of compressible viscoelastic system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yusuke Ishigaki
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Viscoelastic System ◽  
Diffusion Wave ◽  
Estimates Of Solutions ◽  
Whole Space ◽  
Wave Phenomena

<p style='text-indent:20px;'>We consider the large time behavior of solutions of compressible viscoelastic system around a motionless state in a three-dimensional whole space. We show that if the initial data belongs to <inline-formula><tex-math id="M2">\begin{document}$ W^{2,1} $\end{document}</tex-math></inline-formula>, and is sufficiently small in <inline-formula><tex-math id="M3">\begin{document}$ H^4\cap L^1 $\end{document}</tex-math></inline-formula>, the solutions grow in time at the same rate as <inline-formula><tex-math id="M4">\begin{document}$ t^{\frac{1}{2}} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M5">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula> due to diffusion wave phenomena of the system caused by interaction between sound wave, viscous diffusion and elastic wave.</p>

scholarly journals Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Junbai Ren
Keyword(s):  
Weak Solutions ◽  
Large Time ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Heat Semigroup ◽  
Time Behavior ◽  
Decay Estimates ◽  
Navier Stokes Equations

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together withLp-Lqestimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations asC1(1+t)-3/4≤uL2≤C2(1+t)-3/4,  t>1.The decay rate is optimal since it coincides with that of heat equation.

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