scholarly journals On the well-posedness and decay rates of strong solutions to a multi-dimensional non-conservative viscous compressible two-fluid system

2020 ◽  
Vol 40 (5) ◽  
pp. 2515-2559
Author(s):  
Fuyi Xu ◽  
◽  
Meiling Chi ◽  
Lishan Liu ◽  
Yonghong Wu ◽  
...  
Keyword(s):  
Strong Solutions ◽  
Decay Rates ◽  
Well Posedness ◽  
Fluid System ◽  
Two Fluid

The optimal decay estimates on the framework of Besov spaces for the Euler–Poisson two-fluid system

2015 ◽  
Vol 25 (10) ◽  
pp. 1813-1844 ◽  
Author(s):  
Jiang Xu ◽  
Shuichi Kawashima
Keyword(s):  
Besov Spaces ◽  
Hyperbolic Systems ◽  
Low Frequency ◽  
Direct Consequence ◽  
Decay Rates ◽  
Decay Estimates ◽  
Fluid System ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Two Fluid

In this paper, we are concerned with the optimal decay estimates for the Euler–Poisson two-fluid system. It is first revealed that the irrotationality of the coupled electronic field plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta–Kawashima condition. This fact inspires us to obtain decay properties for linearized systems in the framework of Besov spaces. Furthermore, various decay estimates of solution and its derivatives of fractional order are deduced by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As the direct consequence, the optimal decay rates of Lp(ℝ3)-L2 (ℝ3) (1 ≤ p < 2) type for the Euler–Poisson two-fluid system are also shown. Compared with previous works in Sobolev spaces, a new observation is that the difference of variables exactly consists of a one-fluid Euler–Poisson equations, which leads to the sharp decay estimates for velocities.

scholarly journals On global well-posedness and decay of 3D Ericksen-Leslie system

2021 ◽  
Vol 6 (11) ◽  
pp. 12660-12679
Author(s):  
Xiufang Zhao ◽  
◽  
Ning Duan ◽  
Keyword(s):  
Strong Solutions ◽  
Decay Rates ◽  
Well Posedness ◽  
Small Initial Data ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Liquid Crystal System ◽  
The Cauchy Problem ◽  
Derivatives Of ◽  
Leslie System

<abstract><p>In this paper, the small initial data global well-posedness and time decay estimates of strong solutions to the Cauchy problem of 3D incompressible liquid crystal system with general Leslie stress tensor are studied. First, assuming that $ \|u_0\|_{\dot{H}^{\frac12+\varepsilon}}+\|d_0-d_*\|_{\dot{H}^{\frac32+\varepsilon}} $ ($ \varepsilon &gt; 0) $ is sufficiently small, we obtain the global well-posedness of strong solutions. Moreover, the $ L^p $–$ L^2 $ ($ \frac32\leq p\leq2 $) type optimal decay rates of the higher-order spatial derivatives of solutions are also obtained. The $ \dot{H}^{-s} $ ($ 0\leq s &lt; \frac12 $) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates.</p></abstract>

scholarly journals On a model for internal waves in rotating fluids

2018 ◽  
Vol 3 (2) ◽  
pp. 627-648 ◽  
Author(s):  
A. Durán
Keyword(s):  
Internal Waves ◽  
Fluid Model ◽  
Well Posedness ◽  
Solitary Wave Solutions ◽  
Rotating Fluid ◽  
Rotating Fluids ◽  
Mathematical Properties ◽  
Gravity Effects ◽  
Two Fluid Model ◽  
Two Fluid

AbstractIn this paper a rotating two-fluid model for the propagation of internal waves is introduced. The model can be derived from a rotating-fluid problem by including gravity effects or from a nonrotating one by adding rotational forces in the dispersion balance. The physical regime of validation is discussed and mathematical properties of the new system, concerning well-posedness, conservation laws and existence of solitary-wave solutions, are analyzed.

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