Electron. J. Differential Equations, Vol. 2023 (2023), No. 41, pp. 129.
Spacetime decay rates of a twophase flow model with magnetic field in R^3
Qin Ye, Yinghui Zhang
Abstract:
We investigate the spacetime decay rates of strong solution to a
twophase 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 spacetime 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 spacetime decay rate of \(k(0\leq k \leq \ell2)\)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; Twophase flow model; Spacetime 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


Yinghui Zhang
School of Mathematics and Statistics
Guangxi Normal University
Guilin, Guangxi 541004, China
email: yinghuizhang@mailbox.gxnu.edu.cn

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