KRM
Blowup of smooth solutions to the full compressible MHD system with compact density
Baoquan Yuan Xiaokui Zhao
This paper studies the blowup of smooth solutions to the full compressible MHD system with zero resistivity on $\mathbb{R}^{d}$, $d\geq 1$. We obtain that the smooth solutions to the MHD system will blow up in finite time, if the initial density is compactly supported.
keywords: Full compressible MHD system smooth solution blowup.
DCDS-S
Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space
Baoquan Yuan Xiao Li
In this paper, we investigate the blow-up criteria of smooth solutions and the regularity of weak solutions to the micropolar fluid equations in three dimensions. We obtain that if $ \nabla_{h}u,\nabla_{h}\omega\in L^{1}(0,T;\dot{B}^{0}_{\infty,\infty})$ or $ \nabla_{h}u,\nabla_{h}\omega\in L^{\frac{8}{3}}(0,T;\dot{B}^{-1}_{\infty,\infty})$ then the solution $(u,\omega)$ can be extended smoothly beyond $t=T$.
keywords: Micropolar fluid equations blow-up criteria regularity criteria smooth solutions Besov space.
DCDS
Note on the blowup criterion of smooth solution to the incompressible viscoelastic flow
Baoquan Yuan
We study the blowup criterion of smooth solution to the Oldroyd model. Let $(u(t,x), F(t,x)$ be a smooth solution in $[0,T)$, it is shown that the solution $(u(t,x), F(t,x)$ does not appear breakdown until $t=T$ provided $∇ u(t,x)∈ L^1([0,T]; L^∞(\mathbb{R}^n))$ for $n=2,3$.
keywords: Oldroyd model Incompressible viscoelastic fluids blowup criterion of smooth solution.
KRM
A blowup criterion for the 2D $k$-$\varepsilon$ model equations for turbulent flows
Baoquan Yuan Guoquan Qin
We establish a blow up criterion for the two-dimensional $k$-$\varepsilon$ model equations for turbulent flows in a bounded smooth domain $\Omega$. It is shown that for the initial-boundary value problem of the 2D $k$-$\varepsilon$ model equations in a bounded smooth domain, if $\|\nabla u\|_{L^{1}(0, T; L^{\infty})}+\|\nabla\rho\|_{L^{2}(0, T; L^{\infty})} +\|\varepsilon\|_{L^{2}(0, T; L^{\infty})}$ $<\infty$, then the strong solution $(\rho, u, h,k, \varepsilon)$ can be extended beyond $T$.
keywords: $k$-$\varepsilon$ model equations compressible flows turbulence. blow up criterion strong solution

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