• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.215-247
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• 2020

In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neumann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some L^p-estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addition to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.244-262
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• 2022

In this paper, we analyze the hybridizable discontinuous Galerkin (HDG) method for second-order elliptic equations with nonlinear coefficients, which are used in many fields. We present the HDG method that uses a mixed formulation based on numerical trace and flux. Under assumptions on the nonlinear coefficient and H²-regularity for a dual problem, we prove that the discrete systems are well-posed and the numerical solutions have the optimal order of convergence as a mesh parameter. Also, we provide a matrix formulation that can be calculated using an iterative technique for numerical experiments. Finally, we present representative numerical examples in 2D to verify the validity of the proof of Theorem 3.10.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1483-1504
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• 2017

We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.

• Applied Chemistry for Engineering
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• v.20 no.2
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• pp.201-207
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• 2009

The hydrogenation reaction of methyl dodecanoate for the synthesis of 1-dodecanol has been carried out in the presence of a copper chromite catalyst. The catalysts were synthesized by ceramic method, co-precipitation, and improved co-precipitation method and the particles were characterized by SEM and XRD. Also, the products of the reaction were assigned by GC, GC/MSD and NMR. The particles synthesized by each method showed (1) a spherical shape with the size of 3.2 to $7.0{\mu}m$, (2) an agglomerated spherical shape with the size of 50 to 500 nm and (3) a spherical shape with smaller particle size, respectively. Especially, in order to control the size of particles, the particles were synthesized in various dispersant solutions as Span 80, polyacrylate, and polyethyleneglycols (PEGs). The particles synthesized in PEG (Mw = 4000) solution showed the smallest particle size of 30 to 50 nm and the regularity of the particle size distribution. Our experimental results elucidated that the activity of catalyst for hydrogenation increases with decreasing the size of catalyst particle. The highest yield of dodecanol in the hydrogenation reaction was 95.5% when copper chromite synthesized in the PEG solution was used as a catalyst in the optimized reaction condition.