DCDS-B
Meshless method for the stationary incompressible Navier-Stokes equations
Hi Jun Choe Hyea Hyun Kim Do Wan Kim Yongsik Kim
Discrete & Continuous Dynamical Systems - B 2001, 1(4): 495-526 doi: 10.3934/dcdsb.2001.1.495
Mathematical analysis is achieved on a meshless method for the stationary incompressible Stokes and Navier-Stokes equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed. The existence of discrete solution and its error estimate are obtained. As a numerical example for convergence analysis, we compute the numerical solutions for these equations to compare with exact solutions. Also we solve the driven cavity flow numerically as a test problem.
keywords: Meshless method Stokes equations Navier-Stokes equations MLSRK error estimate.
CPAA
Wellposedness of the Keller-Segel Navier-Stokes equations in the critical Besov spaces
Hi Jun Choe Bataa Lkhagvasuren Minsuk Yang
Communications on Pure & Applied Analysis 2015, 14(6): 2453-2464 doi: 10.3934/cpaa.2015.14.2453
We consider the Keller-Segel model coupled with the incompressible Navier-Stokes equations in dimension three. We prove the local in time existence of the solution for large initial data and the global in time existence of the solution for small initial data plus some smallness condition on the gravitational potential in the critical Besov spaces, which are new results for the model.
keywords: critical Besov spaces Keller-Segel model Banach fixed point theorem. incompressible Navier-Stokes equations
DCDS-B
Meshfree method for the non-stationary incompressible Navier-Stokes equations
Hi Jun Choe Do Wan Kim Yongsik Kim
Discrete & Continuous Dynamical Systems - B 2006, 6(1): 17-39 doi: 10.3934/dcdsb.2006.6.17
We consider the solvability and the error estimates of numerical solutions of the non-stationary incompressible Stokes and Navier-Stokes equations by the meshfree method. The moving least square reproducing kernel method or the MLSRK method is employed for the space approximations. The existence of numerical solutions and the $L^2$-type error estimates are obtained. As a numerical example, we compare the numerical solutions of the Stokes and the Navier-Stokes equations with the exact solutions. Also we solve the non-stationary Navier-Stokes driven cavity flow using the MLSRK method.
keywords: MLSRK Stokes Equations Meshfree Method Navier-Stokes Equations Error Estimate.

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