• 대한수학회보
• /
• 제50권3호
• /
• pp.753-760
• /
• 2013

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a bounded Lipschitz do-main under Dirichlet boundary condition. We present by a very simple argument that a strong solution exists globally when the product of $L^2$ norms of the initial velocity and the gradient of the initial velocity and $L^{p,2}$, $p{\geq}4$ norm of the forcing function are small enough. Our condition is scale invariant and implies many typical known global existence results for small initial data including the sharp dependence of the bound on the volumn of the domain and viscosity. We also present a similar result in the whole domain with slightly stronger condition for the forcing.

• 대한수학회보
• /
• 제55권2호
• /
• pp.379-403
• /
• 2018

In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

• 한국전산유체공학회지
• /
• 제1권1호
• /
• pp.64-70
• /
• 1996

Three dimensional turbulent flow fields around ships are simulated by a numerical method. Reynolds Averaged Navier-Stokes equations are used where Reynolds stresses are approximated by Baldwin-Lomax and Sub-Grid Scale(SGS) turbulence models. Body-fitted coordinate system is introduced to conform three dimensional ship geometries. The governing equations are discretized by a finite volume method. Temporal derivatives are approximated by the forward differencing and the convection terms are approximated by the QUICK or Kawamura scheme. The 2nd-order centered differencing is used for other spatial derivatives. Pressure and velocity fields are simultaneously iterated by the Highly Simplified Marker-And-Cell method. To verify the numerical method and turbulence models, flow fields around ships are simulated and compared to the experiments.

• 한국추진공학회지
• /
• 제14권1호
• /
• pp.11-19
• /
• 2010

온도예조건화 나비어스톡스 방정식의 계산오차를 줄이기 위한 방법을 제시하였다. 이 방법은 또한 기존 예조건화 방법론에도 적용하였다. 제시된 방법의 타당성을 검토하기 위하여 다양한 마하수의 원형 실린더 주위의 단열 층류 점성 유동을 계산하였다. 엔탈피의 재정의를 통해 총엔탈피의 크기 정도를 줄임으로써 계산오차에 의한 온도예조건화의 수렴성 문제가 해결됨을 보였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제15권2호
• /
• pp.143-150
• /
• 2011

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a thin periodic domain. We present a simple proof that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$(0,${\infty}$;$L^2$), $2{\leq}p{\leq}{\infty}$ satisfy certain condition. This condition is basically similar to that by Iftimie and Raugel[7], which covers larger and larger initial data and forcing functions as the thickness of the domain ${\epsilon}$ tends to zero.

• 대한수학회지
• /
• 제48권3호
• /
• pp.529-550
• /
• 2011

In this work, a numerical solution of the incompressible Navier-Stokes equations is proposed. The method suggested is based on an algorithm of discretization by mixed finite elements with a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

• 대한수학회지
• /
• 제49권2호
• /
• pp.315-324
• /
• 2012

We consider the global existence of strong solutions of the 3D incompressible Navier-Stokes equations in a long periodic domain. We show by a simple argument that a strong solution exists globally in time when the initial velocity in $H^1$ and the forcing function in $L^p$([0; T);$L^2$), T > 0, $2{\leq}p{\leq}+\infty$ satisfy a certain condition. This condition common appears for the global existence in thin non-periodic domains. Larger and larger initial data and forcing functions satisfy this condition as the thickness of the domain $\epsilon$ tends to zero.

• 대한수학회지
• /
• 제43권1호
• /
• pp.45-63
• /
• 2006

This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.

• Korean Journal of Mathematics
• /
• 제23권2호
• /
• pp.293-312
• /
• 2015

We deal with a boundary control problem for the vorticity minimization, in which the ow is governed by the time-dependent two dimensional incompressible Navier-Stokes equations. We derive a mathematical formulation and a process for an appropriate control along the portion of the boundary to minimize the vorticity motion due to the ow in the fluid domain. After showing the existence of an optimal solution, we derive the optimality system for which optimal solutions may be determined. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solutions.

• Korean Journal of Mathematics
• /
• 제22권4호
• /
• pp.645-658
• /
• 2014

Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.