School of Mathematics and Statistics
Guangxi Normal University
Guilin, Guangxi 541004, China
email: yeqin811@163.com
School of Mathematics and Statistics
Guangxi Normal University
Guilin, Guangxi 541004, China
email: yinghuizhang@mailbox.gxnu.edu.cn
Qin Ye, Yinghui Zhang
Abstract:
We investigate the space-time decay rates of strong solution to a
two-phase flow model with magnetic field in the whole space \(\mathbb{R}^3 \).
Based on the temporal decay results by Xiao [24]
we show that for any integer \(\ell\geq 3\), the space-time decay rate of
\(k(0\leq k \leq \ell)\)-order spatial derivative of the strong solution in
the weighted Lebesgue space \( L_\gamma^2 \) is \(t^{-\frac{3}{4}-\frac{k}{2}+\gamma}\).
Moreover, we prove that the space-time decay rate of \(k(0\leq k \leq \ell-2)\)-order
spatial derivative of the difference between two velocities of the fluid in the
weighted Lebesgue space \( L_\gamma^2 \) is \(t^{-\frac{5}{4}-\frac{k}{2}+\gamma}\),
which is faster than ones of the two velocities themselves.
Submitted September 21, 2022. Published June 23, 2023.
Math Subject Classifications: 35Q31, 35K65, 76N10.
Key Words: Compressible Euler equations; Two-phase flow model; Space-time decay rate; Weighted Sobolev space.
DOI: https://doi.org/10.58997/ejde.2023.41
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Qin Ye School of Mathematics and Statistics Guangxi Normal University Guilin, Guangxi 541004, China email: yeqin811@163.com |
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Yinghui Zhang School of Mathematics and Statistics Guangxi Normal University Guilin, Guangxi 541004, China email: yinghuizhang@mailbox.gxnu.edu.cn |
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