<Publications>

1. Asymptotics of high Reynolds number flows; Prandtl-Batchelor theory, Unimodality, etc.

• (with Okamoto, Hisashi) Prandtl–Batchelor Theory for Kolmogorov Flows. J. Phys. Soc. Jpn. 89, 114401 (2020) open access

• (with Miyaji, Tomoyuki and Okamoto, Hisashi) Unimodal solutions of the generalized Constantin–Lax–Majda equation with viscosity. Jpn. Ind. Appl. Math. 35 (2018), no. 3, 1065–1083.

• (with Miyaji, Tomoyuki and Okamoto, Hisashi) Unimodal patterns appearing in the two-dimensional Navier-Stokes flows under general forcing at large Reynolds numbers. Eur. J. Mech. B Fluids 65 (2017), 234-246.

• (with Okamoto, Hisashi) Unimodal patterns appearing in the Kolmogorov flows at large Reynolds numbers. Nonlinearity 28 (2015), no. 9, 3219-3242. open access

• (with Okamoto, Hisashi) The generalized Proudman-Johnson equation and its singular perturbation problems. Jpn. J. Ind. Appl. Math. 31 (2014), no. 3, 541-573.

• (with Okamoto, Hisashi) The Generalized Proudman-Johnson Equation at large Reynolds numbers. IMA J. Appl. Math (2011) 1-25.

• (with Okamoto, Hisashi) Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds number. Japan J. Industrial Appl. Math. 27 (2010), no. 1, 47-71.

• (with Okamoto, Hisashi) Bifurcations and inviscid limit of rhombic Navier-Stokes flows in tori. IMA J. Appl. Math. 68 (2003), no. 2, 119–134

• (with Childress, Stephen) Vorticity selection with multiple eddies in two-dimensional steady flow at high Reynolds number. SIAM J. Appl. Math. 61 (2001), no. 5, 1605–1617

• On Prandtl-Batchelor theory of a cylindrical eddy: existence and uniqueness. Z. Angew. Math. Phys. 51 (2000), no. 5, 674–686.

• (with Lee, June-Yub) A high-order adaptive numerical method for recirculating flows at large Reynolds number. J. Comput. Appl. Math. 108 (1999), no. 1-2, 75–86.

• Batchelor-Wood formula for negative wall velocity. Phys. Fluids 11 (1999), no. 6, 1685–1687.

• On Prandtl-Batchelor theory of a cylindrical eddy: asymptotic study. SIAM J. Appl. Math. 58 (1998), no. 5, 1394–1413

2. Inviscid limits of fluid related equations

• (with Jeong, In-Jee) On stationary solutions and inviscid limits for generalized Constantin–Lax–Majda equation with O(1) forcing. Nonlinearity 33 (2020), no. 12, 6662-6694. open access

• (with Jeong, In-Jee) On the stationary solutions and inviscid limit for the generalized Proudman-Johnson equation with O(1) forcing. J. Math. Anal. Appl. 472 (2019), no. 1, 842–863.

3. Vortex dynamics in fluid flows; point vortices, vortex patches, vortex sheets, etc.

• (with Sohn, Sung-Ik, Yim, Habin) Motion of three geostrophic Bessel vortices. Phys. D 441 (2022), Paper No. 133509. open access

• (with Sohn, Sung-Ik) Linear stability and nonlinear evolution of a polar vortex cap on a rotating sphere. Eur. J. Mech. B Fluids 85 (2021), 102-109.

• (with Yoon, Jongbin; Yim, Habin) Stuart vortices on a hyperbolic sphere. J. Math. Phys 61 (2020), no. 2, 023103, 17 pp.

• (with Sohn, Sung-Ik and Sakajo, Takashi) Stability of barotropic vortex strip on a rotating sphere. Proc. A. 474 (2018), no. 2210, 20170883, 25 pp.

• (with Hwang, Seungsu) Relative equilibria of point vortices on the hyperbolic sphere. J. Math. Phys. 54 (2013), no. 6, 063101, 15 pp.

• (with Sohn, Sung-Ik) Interactions of three viscous point vortices. J. Phys. A 45 (2012), no. 45, 455501 15 pp.

• Vortex Motion on Riemann Surfaces. J. Korean Physical Soc. 59 (2011), no. 1, 47-54.

• Latitudinal point vortex rings on the spheroid. Proc. R. Soc. 466A (2010) 1749.1768.

• The motion of point vortex dipole on the ellipsoid of revolution. Bull. of Korean Math. Soc. 47 (2010), no. 1, 73-79.

• (with Hwang, Seungsu) Point vortices on hyperbolic sphere. J. Geom. Phys. 59 (2009) 475-488.

• Evolution of a two-dimensional closed vortex sheet in a potential flow. J. Korean Phys. Soc. 46 (2005), 848-854.

• (with Lee, June-Yub and Sohn, Sung-Ik) Long time computation of two-dimensional vortex sheet by point vortex method. J. Phys. Soc. Japan. 72 (2003), no. 8, 1968–1976

4. Complex function theory and applications; conformal mappings, free boundary problems, etc.

• A free-boundary problem for Euler flows with constant vorticity on the sphere. J. Math. Anal. Appl. 465 (2018), no. 1, 703-711.

• (with Okamoto, Hisashi) Uniqueness of the exact solutions of the Navier-Stokes equations having null nonlinearity. Proc. R. Soc. Edinburgh 136A (2006), 1303.1315.

• On the location of critical point for the Poisson equation in plane. J. Math. Anal. Appl. 321 (2006), 213.222.

• Some remarks on free boundaries of recirculating Euler flows with constant vorticity. Inverse problems and related topics (Kobe, 1998), 89–95, Chapman & Hall/CRC Res. Notes Math., 419, Chapman & Hall/CRC, Boca Raton, FL, 2000.

• A free-boundary problem for Euler flows with constant vorticity. Appl. Math. Lett. 12 (1999), no. 4, 101–104.

• A variational approach to the determination of domain for Euler flows with constant vorticity. Korean J. Comput. Appl. Math. 5 (1998), no. 2, 415–421.

5. Others

• (with Ha, Seung-Yeal, et al.) Emergent behaviors of a first-order particle swarm model on the hyperboloid. J. Math. Phys. 61 (2020), no. 4, 042701, 23 pp. 

• (with Chen, Larry, et al.) A rate of convergence for the LANS α regularization of Navier-Stokes equations. J. Math. Anal. Appl. 348 (2008), no 2, 637.649.

• The Oseen-type expansion of Navier-Stokes flows with an application to swimming velocity. Bull. Korean Math. Soc. 38 (2001), no. 2, 337–346.

6. 전공소개

• 소용돌이 동역학(Vortex Dynamics). 대한수학회소식 79 (2001), open access

• Asymptotic Study of Navier-Stokes Flows. Trends in Mathematics, 6 (2003), no. 1, 29-33. open access.

• 콜모고로프 흐름과 단일모드성 추측. 대한수학회소식 195 (2021), open access.

(last updated at 2022.11.04)