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Blowup Mechanism for a Fluid-Particle Interaction System in R3$\mathbb{R}^{3}$
Acta Applicandae Mathematicae ( IF 1.2 ) Pub Date : 2020-04-22 , DOI: 10.1007/s10440-020-00330-0
Jinrui Huang , Bingyuan Huang , Yuqin Wu

We study the Cauchy problem and the mixed initial boundary value problem of a fluid-particle interaction system in \(\mathbb{R}^{3}\). A Serrin type criterion for the strong solution of the Cauchy problem is established in terms of \(\|\rho \|_{L^{\infty }_{t}L^{\infty }_{x}}\) and \(\|u\|_{L^{s}_{t}L^{r}_{x}}\), where \(2/s+3/r\le 1\) and \(3< r\le \infty \). In view of some useful integral inequalities, we prove the life span estimates of the regular solution.



中文翻译:

R3 $ \ mathbb {R} ^ {3} $中流体-颗粒相互作用系统的爆破机理

我们研究了\(\ mathbb {R} ^ {3} \)中流体相互作用系统的柯西问题和混合初始边值问题。根据\(\ | \ rho \ | _ {L ^ {\ infty} _ {t} L ^ {\ infty} _ {x}} \)建立了柯西问题强解的Serrin类型准则。和\(\ | u \ | _ {L ^ {s} _ {t} L ^ {r} _ {x}} \),其中\(2 / s + 3 / r \ le 1 \)\( 3 <r \ le \ infty \)。鉴于一些有用的积分不等式,我们证明了正规解的寿命估计。

更新日期:2020-04-22
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