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2014 | 12 | 10 | 1460-1483
Tytuł artykułu

Partial regularity of solution to generalized Navier-Stokes problem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
10
Strony
1460-1483
Opis fizyczny
Daty
wydano
2014-10-01
online
2014-06-21
Twórcy
Bibliografia
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  • [3] Bulíček, M., Kaplický, P., Incompressible Fluids With Shear Rate and Pressure Dependent Viscosity: Regularity of Steady Planar flows, Discrete Contin. Dyn. Syst. Ser. S 1, no. 1, 41–50 (2008)
  • [4] Bulíček, M., Málek, J., Rajagopal, K. R., Navier’s Slip and Evolutionary Navier-Stokes-like Systems, Indiana University Mathematics Journal, Vol. 56, No.1 (2007)
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  • [7] Evans, L., C., Partial Differential Equations, Graduate studies in Mathematics 19., American Mathematical Society, Providence (1998)
  • [8] Franta, M., Málek, J., Rajagopal, K. R., On Steady Flows of Fluids With Pressure- and Shear-dependent Viscosities, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461,no. 2055, 651–670 (2005) http://dx.doi.org/10.1098/rspa.2004.1360
  • [9] Fučík, S., John, O., Kufner, A., Function Spaces, Noordhoff Internation Publishing, Leyden and Academia, Praha (1997)
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  • [11] Huy, N. D., Stará, J., On Existence and Regularity of Solutions to a Class of Generalized Stationary Stokes Problem, Comment. Math. Univ. Carolin. 47, no. 2, 241–264 (2006)
  • [12] Huy, N., D., On Existence and Regularity of Solutions to Perturbed Systems of Stokes Type, dissertation thesis, Charles University in Prague (2006)
  • [13] Kaplický, P., Málek, J., Stará, J., C 1, α Solutions to a Class of Nonlinear Fluids in two Dimensions - Stationary Dirichlet Problem, J. Math. Sci., 109, no. 5, 1867–1893 (2002) http://dx.doi.org/10.1023/A:1014440207817
  • [14] Kaplický, P., Tichý, J., Boundary Regularity of Flows Under Perfect Slip Boundary Conditions, Cent. Eur. J. Math. 11, no. 7, 1243–1263 (2013)
  • [15] Mácha, V. On a Generalized Stokes Problem, Cent. Eur. J. Math. 9, no. 4, 874–887 (2011) http://dx.doi.org/10.2478/s11533-011-0047-6
  • [16] Málek, J., Mingione, G., Stará, J., Fluids With Pressure Dependent Viscosity, Partial Regularity of Steady Flows, to appear
  • [17] Málek, J., Mingione, G., Stará, J., Fluids With Pressure Dependent Viscosity, Partial Regularity of Steady Flows, Equadiff 2003, Proceedings of the International Conference of Differential Equations, 380–385 (2005)
  • [18] Málek, J., Nečas, J., Rajagopal, K. R., Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities, Arch. Rational Mech. Anal. 165, no. 3, 243–269, (2002) http://dx.doi.org/10.1007/s00205-002-0219-4
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0427-9
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