• 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 $X_1(\mathbb{R}^d)$.

• Journal of computational fluids engineering
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• v.16 no.4
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• pp.72-83
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• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• 유체기계공업학회:학술대회논문집
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• 2000.12a
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• pp.169-175
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• 2000

A design method for transonic turbine blades is developed based on Navier-Stokes equations. The present computing process is done on the four separate steps, 1.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to the aerodynamic performance and are compared with the experimental data.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.771-795
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• 2013

In this paper we consider the Navier-Stokes equations in the half space. Our aim is to construct a mild solution for initial data in $B^{-\alpha}_{{\infty},{\infty}}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1. To do this, we derive the estimate of the Stokes flow with singular initial data in $B^{-\alpha}_{{\infty},q}(\mathbb{R}^n_+)$, 0 < ${\alpha}$ < 1, 1 < $q{\leq}{\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1079-1092
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• 2011

We consider the Newton's method for an direct solver of the optimal control problems of the Navier-Stokes equations. We show that the finite element solutions of the optimal control problem for Stoke equations may be chosen as the initial guess for the quadratic convergence of Newton's algorithm applied to the optimal control problem for the Navier-Stokes equations provided there are sufficiently small mesh size h and the moderate Reynold's number.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.127-132
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• 1999

The inlet pressure build-up at the leading edge of bearings which have discontinuous lubrication surface is analyzed theoretically. The analyses of Inlet pressure build-up is obtained by means of full Navier-stokes equations. Beam-warming method is used to solve navier-stokes equations. The results show that inlet pressure is above atmosphere pressure in front of leading edge of hearing.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.583-592
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• 2016

In this paper, we consider the global existence of strong solutions to the incompressible Navier-Stokes equations on the cubic domain in $R^3$. While the global existence for arbitrary data remains as an important open problem, we here provide with some new observations on this matter. We in particular prove the global existence result when ${\Omega}$ is a cubic domain and initial and forcing functions are some linear combination of functions of at most two variables and the like by decomposing the spectral basis differently.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1205-1219
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• 2011

In this work, a stabilized characteristic finite volume method for the time-dependent Navier-Stokes equations is investigated based on the lowest equal-order finite element pair. The temporal differentiation and advection term are dealt with by characteristic scheme. Stability of the numerical solution is derived under some regularity assumptions. Optimal error estimates of the velocity and pressure are obtained by using the relationship between the finite volume and finite element methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.51-67
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• 1999

The numerical solution of the Navier-Stokes equations in a constricted stepped channel problem has been obtained using a fourth order numerical method. Transformations are made to have a fine grid near the sharp corner and a long channel downstream. The derivatives in the Navier-Stokes equations are replaced by fourth order central differences which result a 29-point computational stencil. A procedure is used to avoid extra numerical boundary conditions near the solid walls. Results have been obtained for Reynolds numbers up to 1000.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.597-621
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• 2016

We present regularity conditions for suitable weak solutions of the Navier-Stokes equations with slip boundary data near the curved boundary. To be more precise, we prove that suitable weak solutions become regular in a neighborhood boundary points, provided the scaled mixed norm $L^{p,q}_{x,t}$ with 3/p + 2/q = 2, $1{\leq}q$ < ${\infty}$ is sufficiently small in the neighborhood.