• Korean Journal of Mathematics
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• v.15 no.2
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• pp.167-170
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• 2007

We present a new apriori estimates for the surface quasi-geostrophic equation. This apriori estimates give a new blow-up criterion which is different from the known Beale-Kato-Majda type criterion.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.243-248
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• 2012

We consider the (possible) finite time blow-up of the smooth solutions of the 3D incompressible Euler equations in a smooth domain or in $R^3$. We derive blow-up criteria in terms of $L^{\infty}$ of the partial component of Hessian of the pressure together with partial component of the vorticity.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.891-907
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• 2020

In this paper, we consider the Cauchy problem to the tropical climate model. We establish the global regularity for the 2D tropical climate model with generalized nonlocal dissipation of the barotropic mode and obtain a multi-logarithmical vorticity blow-up criterion for the 2D tropical climate model without any dissipation of the barotropic mode.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1007-1019
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• 2000

In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

• Geomechanics and Engineering
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• v.37 no.4
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• pp.323-339
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• 2024

If the pressure exerted on the face of a tunnel excavated by TBM exceeds a threshold, it leads to failure of the soil or rock masses ahead of the tunnel face, which results in heaving the ground surface. In the current research, the upper bound method of limit analysis was employed to calculate the blow-out pressure of tunnels excavated in rock masses obeying the Hoek-Brown nonlinear criterion. The results of the proposed method were compared with three-dimensional finite element models, as well as the available methods in the literature. The results show that when σ_ci, m_i, and GSI increase, the blow-out pressure increases as well. By doubling the tunnel diameter, the blow-out pressure reduces up to 54.6%. Also, by doubling the height of the tunnel cover and the surcharge pressure exerted on the ground surface above the tunnel, the blow-out pressure increased up to 74.9% and 5.4%, respectively. With 35% increase in the unit weight of the rock mass surrounding the tunnel, the blow-out pressure increases in the range of 14.8% to 19.6%. The results of the present study were provided in simple design graphs that can easily be used in practical applications in order to obtain the blow-out pressure.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.635-641
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• 2014

The existence and the regularity of the particle trajectory flow X(x, t) along a velocity field u on $\mathbb{R}^n$ are discussed under the BMO-blow-up condition: $${\int}_{0}^{T}{\parallel}{\omega}({\tau}){\parallel}_{BMO}d{\tau}<{\infty}$$ of the vorticity ${\omega}{\equiv}{\nabla}{\times}u$. A comment on our result related with the mystery of turbulence is presented.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1599-1619
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• 2018

In this paper we study the initial value problem of the non-relativistic Vlasov-Darwin system with generalized variables (VDG). We first prove local existence and uniqueness of a nonnegative classical solution to VDG in three space variables, and establish the blow-up criterion. Then we show that it converges to the well-known Vlasov-Poisson system when the light velocity c tends to infinity in a pointwise sense.

• Journal of Welding and Joining
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• v.11 no.1
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• pp.42-51
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• 1993

In this study, investigations were conducted in calculating parameters of elastic-plastic fracture mechanics using single specimen. The validity of these testing methods was judged by the confirmation of multiple specimen method of stop block test. The results were as follows: In order to measure a fracture toughness using the instrumented impact test, two general requirement must be considered; One, setting up proper impact velocity considered the effect of loading and the other, the necessity of low blow test for obtaining true energy by the compliance correction. It was possible to detect a crack initiation point by calculating the compliance changing rate from a load-defection curve. Criterion of a stable crack growth, $T_{mat}$ could be estimated by using key-curve method for a base metal. and combining Kaiser's rebound compliance with Paris-Hutchison's $T_{appl}$ equation for the brittled zone of welding heat affected.at affected.d.