Publication(Printed and refereed journal papers)

 

(1) Regularity Criterion in terms of Pressure for the Navier-Stokes Equations, Nonlinear Analysis-TMA, 46 (2001), 727--735 (with D. Chae).

(2) On the Regularity of Axisymmetric Solutions of the Navier-Stokes Equations, Math. Zeitschrift, 239 (2002), 645671 (with D. Chae).

(3) On the Time Singularity of the modified Navier-Stokes equations Archive. ineq. and application, 1 (2003), 55--59

(4) Local existence and Blow-up criterion of the inhomogeneous Euler equations,

J. Mathematical Fluid mechanics, 5 (2003) 133--169 (with D. Chae)

(5) Global well-posedness in the super-critical dissipative quasi-geostrophic equations, Comm. Math. Phys., 233 (2003), 297--311 (with D. Chae)

(6) Generic solvability for the 3-D Navier-Stokes equations with nonregular force, E. JDE, (2004) 78 1--8

(7) Ergodicity for the dissipative Boussinesque equations J. Statis. Phys. 117 (2004) 929--973 (with M-Y. Wu)

(8) The incompressible limits of viscous polytropic fluids with zero thermal conductivity coefficient, Comm. PDE, 30 (2005) 1169--1189. (with H. Kim)

(9) On regularity criteria in conjunction with the pressure of the Navier-Stokes equations, International Mathematics Research Notices, 2006 id 80762 1--25 (with K. Kang)

(10) On the Interior Regularity of Suitable Weak Solutions to the Navier-Stokes Equations, Comm. PDE. 32 (2007) 11891207.(with D. Chae and K. Kang)

(11) Remarks on the magnetic helicity and energy conservation for ideal magneto-hydrodynamics, Nonlinearity 20 (2007),2681--2689.(with E. Kang)

(12) Interior regularity criteria for suitable weak solutions of the magnetohydrodynamic equations, J. Differential Equations 247(2009), 2310--2330. (with K. Kang)

(13) Notes on the asymptotically self-similar singularities in the Euler and the Navier-Stokes equations, Discrete Contin. Dyn. Syst. 25 (2009), no. 4, 1181--1193.(with D. Chae and K. Kang)

(14) Some regularity criteria for the 3D incompressible magnetohydrodynamics, J. Math. Anal. Appl. 369 (2010), 317322. (with E. Ji)

(15) On the behaviour of Navier-Stokes equations near a possible singular point" Nonlinearity, 23 (2010), 31873197. (with K.Kang)

(16) Compensated Compactness, Separately Convex Functions and Interpolatory Estimates between Riesz Transforms and Haar Projections, Comm. PDE, 36 (2011), 547--601, (with P. Mueller and S. Mueller)

(17) Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations J. Differential Equations, 251 (2011), 2431--2465, (with M, Chae and K. Kang)

(18) Regularizing Model for the 2D MHD Equations with Zero Viscosity Abstract and Applied Analysis, (2012), pp. 1--7, (with E. Kang)

(19) Notes on the geometric regularity criterion of 3D Navier-Stokes system J. Math. Physics, 53 (2012), pp. 16

(20) Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations, Discrete and Conti. Dynam. Systems Series A, 33 (2013), pp. 22712297

(21) Global classical solutions for a compressible fluid-particle interaction model, J. Hyperbolic Differential Equations, in press.(with M. Chae and K. Kang)

 

Publication (Book Chapters and Proceedings)

 

(1) Regularity criteria of the axisymmetric Navier-Stokes equations, Proceedings of The Navier-Stokes equations: theory and numerical methods (Varenna, 2000), Lecture Notes in Pure and Appl. Math., 223, Dekker, New York, (2002), 159-165.(with D. Chae)

(2) On the global well-posedness and stability of the Navier-Stokes and the related equations, Advances in Math. Fluid Mech., "Contributions to Current Challenges in Mathematical Fluid Mechanics", Birkhauser. (2004), 31-51 (with D. Chae)\\

(3) On the axisymmetric Boussinesq equations without swirl component, Trends in Math., 8 (2005) 101104.

 

Preprints

 

(1) Local estimates of weak solutions for steady state non-newtonian fluid flows, (with B. Jin and K. Kang)

(2) Chemotaxis-Haptotaxis Model for Tumor Invasion with Generalized Growth Term, (with E. Kang)

(3) Global solutions to chemotaxis-haptotaxis tumor invasion system with tissue re-establishment (with E. Kang)

(4) Regularity for shear thickening fluids, (with H.-O. Bae, K. Kang and J. Wolf)

(5) Scaling invariant blow-up criteria for simplified versions of Ericksen-Leslie system.

(6) Global existence and temporal decay in Keller-Segel models coupled to fluid equations, (with M. Chae and K. Kang)

(7) Notes on the global well-posedness for the Maxwell-Navier-Stokes system, (with E. Kang)

(8) Global existence of weak and strong solutions to Cucker-Smale-Navier-Stokes equations in R^2, (with Y.-P. Choi)

(9) Traveling Wave Solutions for the Combustion Model of a Shear Flow in a Cylinder, (with E. Kim and E. Kang)

(10) On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics (with D. Chae)