On the global existence and time-decay rates for a parabolic–hyperbolic model arising from chemotaxis

2021 ◽  
pp. 2150078
Author(s):  
Fuyi Xu ◽  
Xinliang Li
Keyword(s):  
Global Existence ◽  
Global Solutions ◽  
Decay Rates ◽  
Hyperbolic Model ◽  
Time Decay ◽  
Low Frequencies ◽  
Dimension Formula ◽  
Fourier Frequency ◽  
The Cauchy Problem ◽  
Time Decay Rates

In this paper, we are concerned with the study of the Cauchy problem for a parabolic–hyperbolic model arising from chemotaxis in any dimension [Formula: see text]. We first prove the global existence of the model in [Formula: see text] critical regularity framework with respect to the scaling of the associated equations. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we also establish the time-decay rates for the constructed global solutions. Our analyses mainly rely on Fourier frequency localization technology and on a refined time-weighted energy inequalities in different frequency regimes.

STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS

1995 ◽  
Vol 05 (03) ◽  
pp. 279-296 ◽  
Author(s):  
MING MEI
Keyword(s):  
Conservation Laws ◽  
Decay Rates ◽  
Asymptotically Stable ◽  
Time Decay ◽  
Shock Condition ◽  
Viscous Conservation Laws ◽  
Time Decay Rates ◽  
Shock Profiles ◽  
Degenerate Shock ◽  
The Stability

This paper is to study the stability of shock profiles for nonconvex scalar viscous conservation laws with the nondegenerate and the degenerate shock conditions by means of an elementary energy method. In both cases, the shock profiles are proved to be asymptotically stable for suitably small initial disturbances. Moreover, in the case of nondegenerate shock condition, time decay rates of asymptotics are also obtained.

scholarly journals Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in $ \mathbb R^3 $

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guochun Wu ◽  
Han Wang ◽  
Yinghui Zhang
Keyword(s):  
Electric Field ◽  
Decay Rates ◽  
Navier Stokes ◽  
Optimal Time ◽  
Poisson System ◽  
Navier Stokes Equation ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
The Cauchy Problem ◽  
Time Decay Rates

<p style='text-indent:20px;'>We are concerned with the Cauchy problem of the 3D compressible Navier–Stokes–Poisson system. Compared to the previous related works, the main purpose of this paper is two–fold: First, we prove the optimal decay rates of the higher spatial derivatives of the solution. Second, we investigate the influences of the electric field on the qualitative behaviors of solution. More precisely, we show that the density and high frequency part of the momentum of the compressible Navier–Stokes–Poisson system have the same <inline-formula><tex-math id="M2">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> decay rates as the compressible Navier–Stokes equation and heat equation, but the <inline-formula><tex-math id="M3">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> decay rate of the momentum is slower due to the effect of the electric field.</p>

scholarly journals Time decay rates for the compressible viscoelastic flows

2017 ◽  
Vol 452 (2) ◽  
pp. 990-1004 ◽  
Author(s):  
Guochun Wu ◽  
Zhensheng Gao ◽  
Zhong Tan
Keyword(s):  
Decay Rates ◽  
Viscoelastic Flows ◽  
Time Decay ◽  
Time Decay Rates

Equations de Schrödinger non linéaires en dimension deux

1979 ◽  
Vol 84 (3-4) ◽  
pp. 327-346 ◽  
Author(s):  
Thierry Cazenave
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Blow Up ◽  
Global Solutions ◽  
Two Dimensions ◽  
Linear Optics ◽  
Non Linear Optics ◽  
Non Linear ◽  
The Cauchy Problem

SynopsisThis paper is devoted to the study of some non linear Schrödinger equations in two dimensions, arising in non linear optics; in particular, it is concerned with solutions to the Cauchy problem. The problem of global existence and regularity of the solutions, the asymptotic behaviour of global solutions, and the blow-up of non global solutions are studied.

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