Chae, Dongho; Wolf, Jörg On the discretely self-similar solutions to the Euler equations in \(\mathbb{R}^3\). (English) Zbl 1526.35257 J. Nonlinear Sci. 33, No. 6, Paper No. 115, 25 p. (2023). MSC: 35Q30 76D03 76D05 35C06 35B53 35B44 35B45 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, J. Nonlinear Sci. 33, No. 6, Paper No. 115, 25 p. (2023; Zbl 1526.35257) Full Text: DOI
Chae, Dongho Anisotropic Liouville type theorem for the stationary Navier-Stokes equations in \(\mathbb{R}^3\). (English) Zbl 07708818 Appl. Math. Lett. 142, Article ID 108655, 5 p. (2023). MSC: 35Q30 76D05 76D03 35A02 PDFBibTeX XMLCite \textit{D. Chae}, Appl. Math. Lett. 142, Article ID 108655, 5 p. (2023; Zbl 07708818) Full Text: DOI
Chae, Dongho; Wolf, Jörg Existence of local suitable weak solutions to the Navier-Stokes equations for initial data in \(L^2_{loc} ( \mathbb{R}^3)\). (English) Zbl 1519.35221 Nonlinear Anal., Real World Appl. 73, Article ID 103892, 28 p. (2023). MSC: 35Q30 76D05 35D30 35B65 35C06 35A01 35A02 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Nonlinear Anal., Real World Appl. 73, Article ID 103892, 28 p. (2023; Zbl 1519.35221) Full Text: DOI arXiv
Chae, Dongho Regularity criterion in terms of the oscillation of pressure for the 3D Navier-Stokes equations. (English) Zbl 1514.35308 Z. Angew. Math. Phys. 74, No. 3, Paper No. 87, 8 p. (2023). MSC: 35Q30 76D05 76D03 35B65 35B50 35B05 35A01 35A02 PDFBibTeX XMLCite \textit{D. Chae}, Z. Angew. Math. Phys. 74, No. 3, Paper No. 87, 8 p. (2023; Zbl 1514.35308) Full Text: DOI
Chae, Dongho; Kim, Junha; Wolf, Jörg On Liouville-type theorems for the stationary MHD and the Hall-MHD systems in \(\mathbb{R}^3\). (English) Zbl 1485.35321 Z. Angew. Math. Phys. 73, No. 2, Paper No. 66, 15 p. (2022). Reviewer: Piotr Biler (Wrocław) MSC: 35Q35 76W05 35B53 76D05 81V70 PDFBibTeX XMLCite \textit{D. Chae} et al., Z. Angew. Math. Phys. 73, No. 2, Paper No. 66, 15 p. (2022; Zbl 1485.35321) Full Text: DOI arXiv
Chae, Dongho; Kim, Junha; Wolf, Jörg On Liouville type theorems in the stationary non-Newtonian fluids. (English) Zbl 1479.35652 J. Differ. Equations 302, 710-727 (2021). MSC: 35Q35 35Q30 76A05 76D05 76D03 35B53 35D30 PDFBibTeX XMLCite \textit{D. Chae} et al., J. Differ. Equations 302, 710--727 (2021; Zbl 1479.35652) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg On Liouville type theorems for the stationary MHD and Hall-MHD systems. (English) Zbl 1470.35255 J. Differ. Equations 295, 233-248 (2021). MSC: 35Q30 76D05 76D03 76W05 81V70 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, J. Differ. Equations 295, 233--248 (2021; Zbl 1470.35255) Full Text: DOI arXiv
Chae, D.; Wolf, J. On the Serrin-type condition on one velocity component for the Navier-Stokes equations. (English) Zbl 1472.35268 Arch. Ration. Mech. Anal. 240, No. 3, 1323-1347 (2021). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 35B65 35D30 76D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Arch. Ration. Mech. Anal. 240, No. 3, 1323--1347 (2021; Zbl 1472.35268) Full Text: DOI arXiv
Chae, Dongho Relative decay conditions on Liouville type theorem for the steady Navier-Stokes system. (English) Zbl 1460.35251 J. Math. Fluid Mech. 23, No. 1, Paper No. 21, 6 p. (2021). MSC: 35Q30 76D05 76D03 35B53 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Fluid Mech. 23, No. 1, Paper No. 21, 6 p. (2021; Zbl 1460.35251) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg On Liouville type theorem for stationary non-Newtonian fluid equations. (English) Zbl 1442.35296 J. Nonlinear Sci. 30, No. 4, 1503-1517 (2020). MSC: 35Q30 76A05 76D05 76D03 35B53 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, J. Nonlinear Sci. 30, No. 4, 1503--1517 (2020; Zbl 1442.35296) Full Text: DOI
Chae, Dongho; Wolf, Jörg Energy concentrations and type I blow-up for the 3D Euler equations. (English) Zbl 1440.35253 Commun. Math. Phys. 376, No. 2, 1627-1669 (2020). MSC: 35Q31 76D05 76B03 35B44 35C06 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Commun. Math. Phys. 376, No. 2, 1627--1669 (2020; Zbl 1440.35253) Full Text: DOI arXiv
Chae, Dongho Note on the Liouville type problem for the stationary Navier-Stokes equations in \(\mathbb{R}^3\). (English) Zbl 1427.35174 J. Differ. Equations 268, No. 3, 1043-1049 (2020). MSC: 35Q30 76D05 76D03 35B40 PDFBibTeX XMLCite \textit{D. Chae}, J. Differ. Equations 268, No. 3, 1043--1049 (2020; Zbl 1427.35174) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg On Liouville type theorem for the stationary Navier-Stokes equations. (English) Zbl 1433.35218 Calc. Var. Partial Differ. Equ. 58, No. 3, Paper No. 111, 11 p. (2019). Reviewer: Il’ya Sh. Mogilevskii (Tver’) MSC: 35Q30 76D05 76D03 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Calc. Var. Partial Differ. Equ. 58, No. 3, Paper No. 111, 11 p. (2019; Zbl 1433.35218) Full Text: DOI
Chae, Dongho; Wolf, Jörg On the local type I conditions for the 3D Euler equations. (English) Zbl 1398.35152 Arch. Ration. Mech. Anal. 230, No. 2, 641-663 (2018). MSC: 35Q31 76D05 35B44 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Arch. Ration. Mech. Anal. 230, No. 2, 641--663 (2018; Zbl 1398.35152) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg Existence of discretely self-similar solutions to the Navier-Stokes equations for initial value in \(L_{\mathrm{loc}}^2(\mathbb{R}^3)\). (English) Zbl 1391.76057 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 4, 1019-1039 (2018). MSC: 76B03 35Q31 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 4, 1019--1039 (2018; Zbl 1391.76057) Full Text: DOI arXiv
Chae, Dongho; Wolf, Joerg On Liouville type theorem for a generalized stationary Navier-Stokes equations. arXiv:1811.09051 Preprint, arXiv:1811.09051 [math.AP] (2018). MSC: 35Q30 76D05 76D03 BibTeX Cite \textit{D. Chae} and \textit{J. Wolf}, ``On Liouville type theorem for a generalized stationary Navier-Stokes equations'', Preprint, arXiv:1811.09051 [math.AP] (2018) Full Text: arXiv OA License
Chae, Dongho; Wolf, Jörg Removing discretely self-similar singularities for the 3D Navier-Stokes equations. (English) Zbl 1386.76023 Commun. Partial Differ. Equations 42, No. 9, 1359-1374 (2017). MSC: 76B03 35Q31 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Commun. Partial Differ. Equations 42, No. 9, 1359--1374 (2017; Zbl 1386.76023) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg On the Liouville type theorems for self-similar solutions to the Navier-Stokes equations. (English) Zbl 1367.35104 Arch. Ration. Mech. Anal. 225, No. 1, 549-572 (2017). MSC: 35Q30 76D05 35C06 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, Arch. Ration. Mech. Anal. 225, No. 1, 549--572 (2017; Zbl 1367.35104) Full Text: DOI arXiv
Chae, Dongho; Lee, Jihoon On the geometric regularity conditions for the 3D Navier-Stokes equations. (English) Zbl 1358.35089 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 151, 265-273 (2017). MSC: 35Q30 76D03 76D05 35B65 35D30 35B44 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 151, 265--273 (2017; Zbl 1358.35089) Full Text: DOI arXiv
Chae, Dongho; Wolf, Jörg On Liouville type theorems for the steady Navier-Stokes equations in \(\mathbb{R}^3\). (English) Zbl 1348.35167 J. Differ. Equations 261, No. 10, 5541-5560 (2016). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Wolf}, J. Differ. Equations 261, No. 10, 5541--5560 (2016; Zbl 1348.35167) Full Text: DOI arXiv
Weng, Shangkun; Chae, Dongho Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations. (English) Zbl 1465.76030 Discrete Contin. Dyn. Syst. 36, No. 10, 5267-5285 (2016). MSC: 76D05 76W05 35B53 35B07 PDFBibTeX XMLCite \textit{S. Weng} and \textit{D. Chae}, Discrete Contin. Dyn. Syst. 36, No. 10, 5267--5285 (2016; Zbl 1465.76030) Full Text: DOI arXiv
Chae, Dongho Remarks on the asymptotically discretely self-similar solutions of the Navier-Stokes and the Euler equations. (English) Zbl 1327.76022 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 251-259 (2015). MSC: 76B03 35Q31 PDFBibTeX XMLCite \textit{D. Chae}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 251--259 (2015; Zbl 1327.76022) Full Text: DOI arXiv
Chae, Dongho Global regularity for a model Navier-Stokes equations on \(\mathbb{R}^3\). (English) Zbl 1322.35062 Analysis, München 35, No. 3, 195-200 (2015). Reviewer: Vladimir Mityushev (Kraków) MSC: 35K55 35Q35 PDFBibTeX XMLCite \textit{D. Chae}, Analysis, München 35, No. 3, 195--200 (2015; Zbl 1322.35062) Full Text: DOI arXiv
Chae, Dongho Remarks on the Liouville type problem in the stationary 3D Navier-Stokes equations. arXiv:1502.04793 Preprint, arXiv:1502.04793 [math.AP] (2015). MSC: 35Q30 76D05 BibTeX Cite \textit{D. Chae}, ``Remarks on the Liouville type problem in the stationary 3D Navier-Stokes equations'', Preprint, arXiv:1502.04793 [math.AP] (2015) Full Text: arXiv OA License
Chae, Dongho Localized energy equalities for the Navier-Stokes and the Euler equations. (English) Zbl 1293.35198 Adv. Math. 254, 69-78 (2014). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q30 35Q31 76D05 PDFBibTeX XMLCite \textit{D. Chae}, Adv. Math. 254, 69--78 (2014; Zbl 1293.35198) Full Text: DOI arXiv
Chae, Dongho Liouville-type theorems for the forced Euler equations and the Navier-Stokes equations. (English) Zbl 1285.35069 Commun. Math. Phys. 326, No. 1, 37-48 (2014). MSC: 35Q31 35Q30 76D05 35B53 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Math. Phys. 326, No. 1, 37--48 (2014; Zbl 1285.35069) Full Text: DOI arXiv
Chae, Dongho; Yoneda, Tsuyoshi On the Liouville theorem for the stationary Navier-Stokes equations in a critical space. (English) Zbl 1306.35082 J. Math. Anal. Appl. 405, No. 2, 706-710 (2013). MSC: 35Q30 35B53 PDFBibTeX XMLCite \textit{D. Chae} and \textit{T. Yoneda}, J. Math. Anal. Appl. 405, No. 2, 706--710 (2013; Zbl 1306.35082) Full Text: DOI
Chae, Dongho On the blow-up problem for the Euler equations and the Liouville type results in the fluid equations. (English) Zbl 1263.76013 Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1139-1150 (2013). MSC: 76B03 76D03 35Q35 PDFBibTeX XMLCite \textit{D. Chae}, Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1139--1150 (2013; Zbl 1263.76013) Full Text: DOI
Chae, Dongho; Constantin, Peter; Wu, Jiahong Dissipative models generalizing the 2D Navier-Stokes and the surface quasi-geostrophic equations. (English) Zbl 1288.35416 Indiana Univ. Math. J. 61, No. 5, 1997-2018 (2012). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 35Q53 35B65 76D03 35Q30 PDFBibTeX XMLCite \textit{D. Chae} et al., Indiana Univ. Math. J. 61, No. 5, 1997--2018 (2012; Zbl 1288.35416) Full Text: DOI arXiv Link
Chae, Dongho Conditions on the pressure for vanishing velocity in the incompressible fluid flows in \(\mathbb{R}^N\). (English) Zbl 1260.35103 Commun. Partial Differ. Equations 37, No. 8, 1445-1455 (2012). MSC: 35Q30 35Q31 76D05 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Partial Differ. Equations 37, No. 8, 1445--1455 (2012; Zbl 1260.35103) Full Text: DOI arXiv
Chae, Dongho On the Liouville type theorems with weights for the Navier-Stokes equations and Euler equations. (English) Zbl 1265.35245 Differ. Integral Equ. 25, No. 3-4, 403-416 (2012). Reviewer: Petr Kaplický (Praha) MSC: 35Q30 35Q31 76B03 76D03 PDFBibTeX XMLCite \textit{D. Chae}, Differ. Integral Equ. 25, No. 3--4, 403--416 (2012; Zbl 1265.35245) Full Text: arXiv
Chae, Dongho Remarks on the Liouville type results for the compressible Navier-Stokes equations in \(\mathbb R^N\). (English) Zbl 1377.76028 Nonlinearity 25, No. 5, 1345-1349 (2012). MSC: 76N10 76N15 35Q30 PDFBibTeX XMLCite \textit{D. Chae}, Nonlinearity 25, No. 5, 1345--1349 (2012; Zbl 1377.76028) Full Text: DOI arXiv
Chae, Dongho Liouville type theorems for the Euler and the Navier-Stokes equations. (English) Zbl 1229.35166 Adv. Math. 228, No. 5, 2855-2868 (2011). Reviewer: Qin Mengzhao (Beijing) MSC: 35Q30 35Q31 76D05 76W05 PDFBibTeX XMLCite \textit{D. Chae}, Adv. Math. 228, No. 5, 2855--2868 (2011; Zbl 1229.35166) Full Text: DOI arXiv
Chae, Dongho On the self-similar solutions of the 3D Euler and the related equations. (English) Zbl 1219.35183 Commun. Math. Phys. 305, No. 2, 333-349 (2011). MSC: 35Q31 35Q30 76D05 35B44 35B40 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Math. Phys. 305, No. 2, 333--349 (2011; Zbl 1219.35183) Full Text: DOI
Chae, Dongho On the uniqueness of solution to the steady Euler equations with perturbations. arXiv:1105.3639 Preprint, arXiv:1105.3639 [math.AP] (2011). MSC: 35Q30 35Q35 76Dxx BibTeX Cite \textit{D. Chae}, ``On the uniqueness of solution to the steady Euler equations with perturbations'', Preprint, arXiv:1105.3639 [math.AP] (2011) Full Text: arXiv OA License
Chae, Dongho On the regularity conditions of suitable weak solutions of the 3D Navier-Stokes equations. (English) Zbl 1195.76146 J. Math. Fluid Mech. 12, No. 2, 171-180 (2010). MSC: 76D03 35Q30 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Fluid Mech. 12, No. 2, 171--180 (2010; Zbl 1195.76146) Full Text: DOI arXiv
Chae, Dongho On the generalized self-similar singularities for the Euler and the Navier-Stokes equations. (English) Zbl 1189.35236 J. Funct. Anal. 258, No. 9, 2865-2883 (2010). MSC: 35Q31 35Q30 76D05 35B45 35B30 35B40 35B44 PDFBibTeX XMLCite \textit{D. Chae}, J. Funct. Anal. 258, No. 9, 2865--2883 (2010; Zbl 1189.35236) Full Text: DOI
Chae, Dongho On the nonexistence of global weak solutions to the Navier-Stokes-Poisson equations in \(\mathbb R^N\). (English) Zbl 1423.35307 Commun. Partial Differ. Equations 35, No. 3, 535-557 (2010). MSC: 35Q35 35A01 35D30 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Partial Differ. Equations 35, No. 3, 535--557 (2010; Zbl 1423.35307) Full Text: DOI arXiv
Chae, Dongho Notes on the incompressible Euler and related equations on \(\mathbb R^N\). (English) Zbl 1189.35235 Chin. Ann. Math., Ser. B 30, No. 5, 513-526 (2009). MSC: 35Q31 35Q30 35B33 35B44 76D03 76N10 PDFBibTeX XMLCite \textit{D. Chae}, Chin. Ann. Math., Ser. B 30, No. 5, 513--526 (2009; Zbl 1189.35235) Full Text: DOI
Chae, Dongho On the behaviors of solutions near possible blow-up time in the incompressible Euler and related equations. (English) Zbl 1260.35134 Commun. Partial Differ. Equations 34, No. 10, 1269-1286 (2009). MSC: 35Q31 35Q30 35B44 76D05 76B03 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Partial Differ. Equations 34, No. 10, 1269--1286 (2009; Zbl 1260.35134) Full Text: DOI arXiv
Chae, Dongho; Kang, Kyungkeun; Lee, Jihoon Notes on the asymptotically self-similar singularitiesin the Euler and the Navier-Stokes equations. (English) Zbl 1179.35208 Discrete Contin. Dyn. Syst. 25, No. 4, 1181-1193 (2009). MSC: 35Q30 35Q31 76D05 76B03 76D03 PDFBibTeX XMLCite \textit{D. Chae} et al., Discrete Contin. Dyn. Syst. 25, No. 4, 1181--1193 (2009; Zbl 1179.35208) Full Text: DOI
Chae, Dongho On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations. (English) Zbl 1173.35094 Adv. Math. 221, No. 5, 1678-1702 (2009). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 35Q30 76D05 35B45 86A05 PDFBibTeX XMLCite \textit{D. Chae}, Adv. Math. 221, No. 5, 1678--1702 (2009; Zbl 1173.35094) Full Text: DOI arXiv
Chae, Dongho Nonexistence of asymptotically self-similar singularities in the Euler and the Navier-Stokes equations. (English) Zbl 1147.35068 Math. Ann. 338, No. 2, 435-449 (2007). Reviewer: Thomas Hagen (Memphis) MSC: 35Q30 35Q35 35B60 76D05 76D03 PDFBibTeX XMLCite \textit{D. Chae}, Math. Ann. 338, No. 2, 435--449 (2007; Zbl 1147.35068) Full Text: DOI arXiv
Chae, Dongho; Kang, Kyungkeun; Lee, Jihoon On the interior regularity of suitable weak solutions to the Navier-Stokes equations. (English) Zbl 1130.35101 Commun. Partial Differ. Equations 32, No. 8, 1189-1207 (2007). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 PDFBibTeX XMLCite \textit{D. Chae} et al., Commun. Partial Differ. Equations 32, No. 8, 1189--1207 (2007; Zbl 1130.35101) Full Text: DOI
Chae, Dongho Nonexistence of self-similar singularities for the 3D incompressible Euler equations. (English) Zbl 1157.35079 Commun. Math. Phys. 273, No. 1, 203-215 (2007). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35Q05 76B03 35B40 35Q30 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Math. Phys. 273, No. 1, 203--215 (2007; Zbl 1157.35079) Full Text: DOI arXiv
Chae, Dongho On the regularity conditions for the Navier-Stokes and related equations. (English) Zbl 1130.35100 Rev. Mat. Iberoam. 23, No. 1, 371-384 (2007). Reviewer: Iuliana Oprea (Fort Collins) MSC: 35Q30 76D03 76D05 PDFBibTeX XMLCite \textit{D. Chae}, Rev. Mat. Iberoam. 23, No. 1, 371--384 (2007; Zbl 1130.35100) Full Text: DOI EuDML
Chae, Dongho On the finite-time singularities of the 3D incompressible Euler equations. (English) Zbl 1124.35048 Commun. Pure Appl. Math. 60, No. 4, 597-617 (2007). Reviewer: Oleg Dementiev (Chelyabinsk) MSC: 35Q05 35Q30 35A20 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Pure Appl. Math. 60, No. 4, 597--617 (2007; Zbl 1124.35048) Full Text: DOI
Chae, Dongho WITHDRAWN: Global regularity for the 3D Navier-Stokes and the 3D Euler equations. arXiv:0711.2453 Preprint, arXiv:0711.2453 [math.AP] (2007); retraction notice ibid. MSC: 35Q30 76B03 76D05 BibTeX Cite \textit{D. Chae}, ``WITHDRAWN: Global regularity for the 3D Navier-Stokes and the 3D Euler equations'', Preprint, arXiv:0711.2453 [math.AP] (2007); retraction notice ibid. Full Text: arXiv
Chae, Dongho On the blow-up problem and new a priori estimates for the 3D Euler and the Navier-Stokes equations. arXiv:0711.1113 Preprint, arXiv:0711.1113 [math.AP] (2007). MSC: 35Q30 76B03 76D05 BibTeX Cite \textit{D. Chae}, ``On the blow-up problem and new a priori estimates for the 3D Euler and the Navier-Stokes equations'', Preprint, arXiv:0711.1113 [math.AP] (2007) Full Text: arXiv
Chae, Dongho On the incompressible Euler equations and the blow-up problem. (English) Zbl 1173.35587 Kozono, Hideo (ed.) et al., Asymptotic analysis and singularities. Hyperbolic and dispersive PDEs and fluid mechanics. Papers of the 14th International Research Institute of the Mathematical Society of Japan (MSJ), Sendai, Japan, July, 18–27, 2005. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-40-2/hbk). Advanced Studies in Pure Mathematics 47-1, 1-30 (2006). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35L65 35L45 35L67 35A07 35Q35 76B03 PDFBibTeX XMLCite \textit{D. Chae}, Adv. Stud. Pure Math. 47--1, 1--30 (2006; Zbl 1173.35587)
Chae, Dongho On the conditional regularity of the Navier-Stokes and related equations. (English) Zbl 1110.35312 Biler, Piotr (ed.) et al., Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 74, 117-126 (2006). MSC: 35Q35 76B03 76D05 PDFBibTeX XMLCite \textit{D. Chae}, Banach Cent. Publ. 74, 117--126 (2006; Zbl 1110.35312)
Chae, Dongho WITHDRAWN: Note on the finite time singularities for the 3D Navier-Stokes equations. arXiv:math/0504219 Preprint, arXiv:math/0504219 [math.AP] (2005); retraction notice ibid. MSC: 35Q30 76D05 76D03 BibTeX Cite \textit{D. Chae}, ``WITHDRAWN: Note on the finite time singularities for the 3D Navier-Stokes equations'', Preprint, arXiv:math/0504219 [math.AP] (2005); retraction notice ibid. Full Text: arXiv
Chae, Dongho On the dual systems to Euler and Navier-Stokes equations in \(\mathbb R^3\). (English) Zbl 1078.76017 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 460, No. 2044, 1153-1168 (2004). MSC: 76D03 76B03 35Q30 35Q35 PDFBibTeX XMLCite \textit{D. Chae}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 460, No. 2044, 1153--1168 (2004; Zbl 1078.76017) Full Text: DOI
Chae, Dongho; Lee, Jihoon On the global well-posedness and stability of the Navier-Stokes and the related equations. (English) Zbl 1083.35086 Galdi, Giovanni P. (ed.) et al., Contributions to current challenges in mathematical fluid mechanics. Basel: Birkhäuser (ISBN 3-7643-7104-8/hbk). Advances in Mathematical Fluid Mechanics, 31-51 (2004). Reviewer: Daniel Ševčovič (Bratislava) MSC: 35Q30 76D03 35-02 37L05 37L15 35D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, in: Contributions to current challenges in mathematical fluid mechanics. Basel: Birkhäuser. 31--51 (2004; Zbl 1083.35086)
Chae, Dongho; Lee, Jihoon On the regularity of the axisymmetric solutions of the Navier-Stokes equations. (English) Zbl 0992.35068 Math. Z. 239, No. 4, 645-671 (2002). MSC: 35Q30 76D03 76D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, Math. Z. 239, No. 4, 645--671 (2002; Zbl 0992.35068) Full Text: DOI
Chae, Dongho; Lee, Jihoon Regularity criteria of the axisymmetric Navier-Stokes equations. (English) Zbl 0991.35063 Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 159-165 (2002). MSC: 35Q30 35B65 35B45 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, Lect. Notes Pure Appl. Math. 223, 159--165 (2002; Zbl 0991.35063)
Chae, Dongho; Lee, Jihoon Regularity criterion in terms of pressure for the Navier-Stokes equations. (English) Zbl 1007.35064 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 46, No. 5, 727-735 (2001). Reviewer: Oleg Titow (Berlin) MSC: 35Q30 76D03 76D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{J. Lee}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 46, No. 5, 727--735 (2001; Zbl 1007.35064) Full Text: DOI
Chae, Dongho; Choe, Hi-Jun Regularity of solutions to the Navier-Stokes equation. (English) Zbl 0923.35117 Electron. J. Differ. Equ. 1999, Paper No. 5, 7 p. (1999). Reviewer: V.A.Sava (Iaşi) MSC: 35Q30 35B65 76B99 PDFBibTeX XMLCite \textit{D. Chae} and \textit{H.-J. Choe}, Electron. J. Differ. Equ. 1999, Paper No. 5, 7 p. (1999; Zbl 0923.35117) Full Text: EuDML EMIS
Chae, Dongho; Kim, Sang-Moon; Kim, Sung-Ki A different proof of the existence theorem on the Navier-Stokes equations. (English) Zbl 0872.35082 J. Korean Math. Soc. 33, No. 4, 1129-1137 (1996). Reviewer: A.Carabineanu (Bucureşti) MSC: 35Q30 76D05 35D05 PDFBibTeX XMLCite \textit{D. Chae} et al., J. Korean Math. Soc. 33, No. 4, 1129--1137 (1996; Zbl 0872.35082)
Chae, Dongho; Dubovskiǐ, Pavel Travelling wave-like solutions of the Navier-Stokes and the related equations. (English) Zbl 0874.35084 J. Math. Anal. Appl. 204, No. 3, 930-939 (1996). MSC: 35Q30 35B40 76D05 PDFBibTeX XMLCite \textit{D. Chae} and \textit{P. Dubovskiǐ}, J. Math. Anal. Appl. 204, No. 3, 930--939 (1996; Zbl 0874.35084) Full Text: DOI
Chae, Dongho; Dubovskiĭ, Pavel Functional and measure-valued solutions of the Euler equations for flows of incompressible fluids. (English) Zbl 0834.76012 Arch. Ration. Mech. Anal. 129, No. 4, 385-396 (1995). Reviewer: J.T.Heynatz (Germering) MSC: 76B47 35Q35 PDFBibTeX XMLCite \textit{D. Chae} and \textit{P. Dubovskiĭ}, Arch. Ration. Mech. Anal. 129, No. 4, 385--396 (1995; Zbl 0834.76012) Full Text: DOI
Kim, Namkwon; Chae, Dongho On the uniqueness of the unbounded classical solutions of the Navier- Stokes and associated equations. (English) Zbl 0810.35079 J. Math. Anal. Appl. 186, No. 1, 91-96 (1994). MSC: 35Q30 35A05 PDFBibTeX XMLCite \textit{N. Kim} and \textit{D. Chae}, J. Math. Anal. Appl. 186, No. 1, 91--96 (1994; Zbl 0810.35079) Full Text: DOI
Chae, Dongho; Foias, Ciprian On the homogeneous statistical solutions of the 2-D Navier-Stokes equations. (English) Zbl 0801.35104 Indiana Univ. Math. J. 43, No. 1, 177-185 (1994). Reviewer: C.Foias (Bloomington) MSC: 35Q30 35R60 PDFBibTeX XMLCite \textit{D. Chae} and \textit{C. Foias}, Indiana Univ. Math. J. 43, No. 1, 177--185 (1994; Zbl 0801.35104) Full Text: DOI
Chae, Dongho Weak solutions of 2-D Euler equations with initial vorticity in \(L(\log L\)). (English) Zbl 0854.35082 J. Differ. Equations 103, No. 2, 323-337 (1993). MSC: 35Q05 35Q30 35L60 PDFBibTeX XMLCite \textit{D. Chae}, J. Differ. Equations 103, No. 2, 323--337 (1993; Zbl 0854.35082) Full Text: DOI
Chae, Dongho Remarks on the regularity of weak solutions of the Navier-Stokes equations. (English) Zbl 0770.35053 Commun. Partial Differ. Equations 17, No. 7-8, 1267-1285 (1992). Reviewer: J.Stará (Praha) MSC: 35Q30 35B65 35D10 76D05 PDFBibTeX XMLCite \textit{D. Chae}, Commun. Partial Differ. Equations 17, No. 7--8, 1267--1285 (1992; Zbl 0770.35053) Full Text: DOI
Chae, Dongho Some a priori estimates for weak solutions of the 3-D Navier-Stokes equations. (English) Zbl 0755.35085 J. Math. Anal. Appl. 167, No. 1, 236-244 (1992). Reviewer: I.Sh.Mogilevskij (Tver) MSC: 35Q30 35B45 76D05 35D10 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Anal. Appl. 167, No. 1, 236--244 (1992; Zbl 0755.35085) Full Text: DOI
Chae, Dongho On the ensemble average in the study of approximate inertial manifolds. II. (English) Zbl 0799.35176 J. Math. Anal. Appl. 164, No. 2, 337-349 (1992). MSC: 35Q30 35B40 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Anal. Appl. 164, No. 2, 337--349 (1992; Zbl 0799.35176) Full Text: DOI
Chae, Dongho The vanishing viscosity limit of statistical solutions of the Navier- Stokes equations. II: The general case. (English) Zbl 0732.35070 J. Math. Anal. Appl. 155, No. 2, 460-484 (1991). Reviewer: Y.R.Romanovsky (Pereslavl-Zalessky) MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Anal. Appl. 155, No. 2, 460--484 (1991; Zbl 0732.35070) Full Text: DOI
Chae, Dongho The vanishing viscosity limit of statistical solutions of the Navier- Stokes equations. I: 2-D periodic case. (English) Zbl 0732.35069 J. Math. Anal. Appl. 155, No. 2, 437-459 (1991). Reviewer: Y.R.Romanovsky (Pereslavl-Zalessky) MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Anal. Appl. 155, No. 2, 437--459 (1991; Zbl 0732.35069) Full Text: DOI
Chae, Dongho On the ensemble average in the study of approximate inertial manifolds. (English) Zbl 0799.35175 J. Math. Anal. Appl. 160, No. 1, 236-249 (1991). MSC: 35Q30 35B40 PDFBibTeX XMLCite \textit{D. Chae}, J. Math. Anal. Appl. 160, No. 1, 236--249 (1991; Zbl 0799.35175) Full Text: DOI