Attractors and their stability with respect to rotational inertia for nonlocal extensible beam equations
May 2020, 40(5): 2515-2559. doi: 10.3934/dcds.2020140
On the well-posedness and decay rates of strong solutions to a multi-dimensional non-conservative viscous compressible two-fluid system
Fuyi Xu 1,, , Meiling Chi 1, , Lishan Liu 2, and Yonghong Wu 3,
School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, Shandong, China
School of Mathematical Science, Qufu Normal University, Qufu, 263516, Shandong, China
Department of Mathematics and Statistics, Curtin University, Perth, 6845, WA, Australia
* Corresponding author: Fuyi Xu
Received October 2018 Revised July 2019 Published March 2020
Fund Project: The first author is supported by the National Natural Science Foundation of China (11501332, 11771043, 11871302, 51976112), the Natural Science Foundation of Shandong Province (ZR2015AL007), and Young Scholars Research Fund of Shandong University of Technology
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The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the scaling of the associated equations. In the functional setting as close as possible to the physical energy spaces, we prove the unique global solvability of strong solutions close to a stable equilibrium state. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we establish the time decay rates for the constructed global solutions. The proof relies on an application of Fourier analysis to a complicated parabolic-hyperbolic system, and on a refined time-weighted inequality.
Keywords: Well-posedness, decay rates, non-conservative viscous compressible two-fluid system, Besov spaces.
Mathematics Subject Classification: Primary: 76T10, 76N10.
Citation: Fuyi Xu, Meiling Chi, Lishan Liu, Yonghong Wu. On the well-posedness and decay rates of strong solutions to a multi-dimensional non-conservative viscous compressible two-fluid system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (5) : 2515-2559. doi: 10.3934/dcds.2020140
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Fuyi Xu Meiling Chi Lishan Liu Yonghong Wu
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