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LOCAL REGULARITY CRITERIA OF THE NAVIER-STOKES EQUATIONS WITH SLIP BOUNDARY CONDITIONS
Bae, Hyeong-Ohk,Kang, Kyungkeun,Kim, Myeonghyeon Korean Mathematical Society 2016 대한수학회지 Vol.53 No.3
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.
MATHEMATICAL MODEL FOR VOLATILITY FLOCKING WITH A REGIME SWITCHING MECHANISM IN A STOCK MARKET
( Hyeong Ohk Bae ),( Seung Yeal Ha ),( Yong Sik Kim ),( Sang Hyeok Lee ),( Hyun Cheul Lim ),( Jane Yoo ) 한국금융공학회 2014 한국금융공학회 학술발표회 Vol.2014 No.1
We present a mathematical model for volatility okcing in a stock market. Our proposed model consists of geometric Brownian motions with time-varying volatilities coupled through the Cucker-Smale ocking and regime switching mechanisms. For the all- to-all interactions where all assets` volatilities are coupled with each other with a constant interaction weight, we show that the common volatility emerges asymptotically, and discuss its _nancial applications. We also provide several numerical simulations and compare them with analytical results.
Bae, Hyeong-Ohk,Jin, Bum-Ja Korean Mathematical Society 2012 대한수학회지 Vol.49 No.1
We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uniform bound of the velocity field and its derivatives.
A Regularity Criterion for the Navier-Stokes Equations
Bae, Hyeong-Ohk,Choe, Hi Jun Marcel Dekker, Inc 2007 Communications in partial differential equations Vol.32 No.7
<P> We prove that a weak solution u = (u1, u2, u3) to the Navier-Stokes equations is strong, if any two components of u satisfy Prodi-Ohyama-Serrin's criterion. As a local regularity criterion, we prove u is bounded locally if any two components of the velocity lie in L6, ∞.</P>
BOUNDARY POINTWISE ERROR ESTIMATE FOR FINITE ELEMENT METHOD
Bae, Hyeong-Ohk,Chu, Jeong-Ho,Choe, Hi-Jun,Kim, Do-Wan Korean Mathematical Society 1999 대한수학회지 Vol.36 No.6
This paper is devoted to the point wise error estimate up to boundary for the standard finite element solution of Poisson equation with Dirichlet boundary condition. Our new approach used the discrete maximum principle for the discrete harmonic solution. once the mesh in our domain satisfies the $\beta$-condition defined by us, the discrete harmonic solution with dirichlet boundary condition has the discrete maximum principle and the pointwise error should be bounded by L-errors newly obtained.
Regularity and singularity of weak solutions to ostwald-de waele flows
BAE, HYEONG-OHK,CHOE, HI JUN,KIM, DO WAN 대한수학회 2000 대한수학회지 Vol.37 No.6
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