• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.339-345
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• 2020

This note deals with the question of the regularity of (Leray) weak solutions of the Navier-Stokes equations in terms of the pressure. This criterion improves on the existing results.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.619-626
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• 2015

This paper considers regularity for the p-harmonic and Ostwald-de Waele flows. Some Serrin's type regularity criteria are established for 1 < p < 2.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.957-975
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• 2000

We find a regularity criterion for the Ostwald-de Waele models like Serrin's condition to the Navier-Stokes equations. Moreover, we show short time existence and estimate the Hausdorff dimension of the set of singular times for the weak solutions.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.557-569
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• 2009

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular up to the boundary if the scaled $L^{\frac{5}{2}}$-norm of the solution is small near the boundary. Our result is also valid in the interior.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.537-558
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• 2008

Consider a weak solution u of the Navier-Stokes equations in the class $L^2((0,T);X_1(\mathbb{R}^d)^d)$. We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space $X_1(\mathbb{R}^d)$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.649-660
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• 2020

This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂_iu₁; ∂_ju₂; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊₃ := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.29 no.4
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• pp.517-529
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• 2019

Introduction: Although shift work is an inevitable form of labor in modern society, it has been identified as a cause of many ailments, such as cancer and musculoskeletal disorders. Meanwhile, previous studies have also shown that musculoskeletal disorders account for a large proportion of total industrial accidents and a high prevalence rate of these ailments has been found in shift workers. Methods: Among the respondents to the 5th Korea Working Conditions Survey(KWCS) 3,916 shift workers(2,658 of whom have not experienced musculoskeletal pain and 1,258 who have experienced musculoskeletal pain) were asked how the work regularity of shift workers affected musculoskeletal pain. Results: The results of a dichotomous logistic regression by correcting the demographic characteristics of the study subjects showed a lower prevalence of musculoskeletal pain in the 'High' regularity group compared to the 'Intermediate' regularity group for the criterion 'Regularity of Time Fixation'. A lower prevalence of musculoskeletal pain was shown in the 'High' and 'Moderate' regularity group compared to the 'Very Low' regularity one. Conclusions: Based on these findings, it was found that musculoskeletal pain occurs less when the work regularity of shift workers is 'Very high' or 'Intermediate', and the effect of working regularity on musculoskeletal pain varies for each shift type of work. It is deemed that more precise observation and understanding are required when managing the working environment of shift workers, and further study of regarding this issue is needed.

• 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: $${\int}_{0}^{T}{\parallel}{\omega}({\tau}){\parallel}_{BMO}d{\tau}&lt;{\infty}$$ of the vorticity ${\omega}{\equiv}{\nabla}{\times}u$. A comment on our result related with the mystery of turbulence is presented.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1996.06a
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• pp.217-220
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• 1996

This paper describes a new hierarchial block matching algorithm especially appropriate for a large search area. The proposed algorithm consists of higher level search for an initial motion vector estimate by using a new matching criterion over the evenly subsampled search points, and lower level search for the final motion vector refinement. In the higher level matching criterion, mean absolute differences at the search points (or motion vector candidates) similar to motion vectors of causally neighboring blocks, are weighted properly so that these points can have a higher chance to being selected. The proposed algorithm outperforms existing hierarchical block matching algorithms, and its computational regularity makes hardware implementation simple.