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REGULARITY CRITERIA FOR THE p-HARMONIC AND OSTWALD-DE WAELE FLOWS
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 Title & Authors
REGULARITY CRITERIA FOR THE p-HARMONIC AND OSTWALD-DE WAELE FLOWS
Fan, Jishan; Nakamura, Gen; Zhou, Yong;
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 Abstract
This paper considers regularity for the p-harmonic and Ostwald-de Waele flows. Some Serrin`s type regularity criteria are established for 1 < p < 2.
 Keywords
p-harmonic flow;regularity criterion;weak solutions;
 Language
English
 Cited by
1.
On scattering of a material over the Ostwald-de Waele fluid bed, The European Physical Journal Plus, 2016, 131, 12  crossref(new windwow)
 References
1.
J. Azzam and J. Bedrossian, Bounded mean oscillation and the uniqueness of active scalar equations, arXiv: 1108.2735 v2[math. AP] 3 Nov 2012.

2.
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.

3.
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).

4.
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. crossref(new window)

5.
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. crossref(new window)

6.
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. crossref(new window)

7.
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.

8.
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. crossref(new window)

9.
L. Diening and M. Ruzicka, Strong solutions for generalized Newtonian fluids, J. Math. Fluid Mech. 7 (2005), no. 3, 413-450. crossref(new window)

10.
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.

11.
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. crossref(new window)

12.
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. crossref(new window)

13.
C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137-193. crossref(new window)

14.
N. Hungerbuhler, Global weak solutions of the p-harmonic flow into homogeneous space, Indiana Univ. Math. J. 45 (1996), no. 1, 275-288.

15.
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.

16.
O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, 2nd edn. Gordon and Breach, New York, 1969.

17.
J. Malek, J. Necas, M. Rokyta, and M. Ruzicka, Weak and Measure-valued Solutions to Evolutionary PDEs, Chapman & Hall, 1996.

18.
M. Misawa, On the p-harmonic flow into spheres in the singular case, Nonlinear Anal. 50 (2002), no. 4, 485-494. crossref(new window)

19.
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. crossref(new window)

20.
M. Pokorny, Cauchy problem for the non-Newtonian viscous incompressible fluid, Appl. Math. 41 (1996), no. 3, 169-201.

21.
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. crossref(new window)