• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.76-107
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• 2022

In this paper, we study the temporal decay of global weak solutions to the inhomogeneous Hall-magnetohydrodynamic (Hall-MHD) equations. First, an approximation problem and its weak solutions are obtained via the Caffarelli-Kohn-Nirenberg retarded mollification technique. Then, we prove that the approximate solutions satisfy uniform decay estimates. Finally, using the weak convergence method, we construct weak solutions with optimal decay rates to the inhomogeneous Hall-MHD equations.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.637-669
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• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.591-598
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• 2018

This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.3
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• pp.647-656
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• 2013

Taking into account the flexoelectric effects, we consider a gradient flow of Landau-de Gennes energy which generalizes the Oseen-Frank energy. In this article, we discuss existence of weak solutions of the gradient flow in an appropriate function space.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.945-966
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• 2017

The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.

• 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.

• 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.51 no.3
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• pp.789-801
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• 2014

In this paper, we study the existence of ground state solutions for a class of non-resonant cooperative elliptic systems by a variant weak linking theorem. Here the classical Ambrosetti-Rabinowitz superquadratic condition is replaced by a general super quadratic condition.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.11-24
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• 2017

Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.

• Restorative Dentistry and Endodontics
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• v.17 no.1
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• pp.115-125
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• 1992

It is advisable to use irrigation solutions which have strong antibacterial effect and weak cytotoxic effect on treating root infections. Streptococci are ones of the most frequently isolated microorganisms in infected root canals. The antibacterial effect of ten irrigation solutions were investigated on S. mutans (19449), S. sanguis. )10556) and 4 streptococci isolated from saliva of healthy persons. These streptococci were exposured to irrigation solutions during 10 sec, 30 sec,. 1 min, 3 min, 5 min, 10 min, 30 min and 2hrs respectively. Four irrigation solutions which showed strong antibacterial activity were diluted to 1 : 1 to 1 : 10,000. Then they were subcultured on blood agar plate an observed after 1 day. 5.25% NaOC1 had the strongest antibacterial effect. 30% urea and normal saline showed no antibacterial effect. 50 % citric acid and 3% $H_2O_2$ showed relatively weak antibacterial effect. 15 % EDTA had very weak antibacterial effect.