연구 과제 주관 기관 : King Abdulaziz University
- J. Azzam and J. Bedrossian, Bounded mean oscillation and the uniqueness of active scalar equations, arXiv: 1108.2735 v2[math. AP] 3 Nov 2012.
- H.-O. Bae, H. J. Choe, and D. W. Kim, Regularity and singularity of weak solutions to Ostwald-De Waele flows, J. Korean Math. Soc. 37 (2000), no. 6, 957-975.
- H.-O. Bae, K. Kang, J. Lee, and J. Wolf, Regularity for Ostwald-de Waele type shear thickening fluids, Nonlinear Differ. Equ. Appl. 2014(in press).
- L. C. Berselli, L. Diening, and M. Ruzicka, Existence of strong solutions for incom- pressible fluids with shear dependent viscosities, J. Math. Fluid Mech. 12 (2010), no. 1, 101-132. https://doi.org/10.1007/s00021-008-0277-y
- M. Bertsch, R. dal Passo, and R. van der Hout, Nonuniqueness for the heat flow of harmonic maps on the disk, Arch. Ration. Mech. Anal. 161 (2002), no. 2, 93-112. https://doi.org/10.1007/s002050100171
- M. Bertsch, R. dal Passo, and A. Pisante, Point singularities and nonuniqueness for the heat flow for harmonic maps, Comm. Partial Differential Equations 28 (2003), no. 5-6, 1135-1160. https://doi.org/10.1081/PDE-120021189
- K.-C. Chang, W.-Y. Ding, and R. Ye, Finite time blow-up of heat flow of harmonic maps from surface, J. Differential Geom. 36 (1992), no. 2, 507-515.
- Y. Chen, M-C. Hong, and N. Hungerbuhler, Heat flow of p-harmonic maps with values into spheres, Math. Z. 215 (1994), no. 1, 25-35. https://doi.org/10.1007/BF02571698
- L. Diening and M. Ruzicka, Strong solutions for generalized Newtonian fluids, J. Math. Fluid Mech. 7 (2005), no. 3, 413-450. https://doi.org/10.1007/s00021-004-0124-8
- L. Diening, M. Ruzicka, and J. Wolf, Existence of weak solutions for unsteady motions of generalized Newtonian fluid, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 (2010), no. 1, 1-46.
- J. Fan and T. Ozawa, Logarithmically improved regularity criteria for Navier-Stokes and related equations, Math. Methods Appl. Sci. 32 (2009), no. 17, 2309-2318. https://doi.org/10.1002/mma.1140
- A. Fardoun and R. Regbaoui, Heat flow for p-harmonic maps with small initial data, Calc. Var. Partial Differential Equations 16 (2003), no. 1, 1-16. https://doi.org/10.1007/s005260100138
C. Fefferman and E. M. Stein,
$H^p$spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137-193. https://doi.org/10.1007/BF02392215
- N. Hungerbuhler, Global weak solutions of the p-harmonic flow into homogeneous space, Indiana Univ. Math. J. 45 (1996), no. 1, 275-288.
R. G. Iagar and S. Moll, Rotationally symmetric p-harmonic flows from
$D^2$to $S^2$: local well-posedness and finite time blow-up, arXiv:1305.6552v1[math.AP], 2013.
- O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, 2nd edn. Gordon and Breach, New York, 1969.
- J. Malek, J. Necas, M. Rokyta, and M. Ruzicka, Weak and Measure-valued Solutions to Evolutionary PDEs, Chapman & Hall, 1996.
- M. Misawa, On the p-harmonic flow into spheres in the singular case, Nonlinear Anal. 50 (2002), no. 4, 485-494. https://doi.org/10.1016/S0362-546X(01)00755-6
- T. Ogawa, Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow, SIAM J. Math. Anal. 34 (2003), no. 6, 1318-1330. https://doi.org/10.1137/S0036141001395868
- M. Pokorny, Cauchy problem for the non-Newtonian viscous incompressible fluid, Appl. Math. 41 (1996), no. 3, 169-201.
- J. Wolf, Existence of weak solutions to the equations of non-stationary motion of non-Newtonian fluids with shear rate dependent viscosity, J. Math. Fluid Mech. 9 (2007), no. 1, 104-138. https://doi.org/10.1007/s00021-006-0219-5
- On scattering of a material over the Ostwald-de Waele fluid bed vol.131, pp.12, 2016, https://doi.org/10.1140/epjp/i2016-16440-8