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Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

For an evolutionary nonlinear fluid model characterized by the viscosity being a decreasing function of the modulus of the symmetric velocity gradient we establish the global-in-time existence of the solution with the Hölder continuous velocity gradients. Such a solution is unique in the class of weak solutions. We deal with the two dimensional space periodic problem.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague 8, Czech Republic, e-mail: kaplicky@karlin.mff.cuni.cz, , , , , , CZ

    P. Kaplický

  2. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague 8, Czech Republic, e-mail: malek@karlin.mff.cuni.cz, , , , , , CZ

    J. Málek

  3. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague 8, Czech Republic, e-mail: stara@karlin.mff.cuni.cz, , , , , , CZ

    J. Stará

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  1. P. Kaplický
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  2. J. Málek
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  3. J. Stará
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Kaplický, P., Málek, J. & Stará, J. Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities. NoDEA, Nonlinear differ. equ. appl. 9, 175–195 (2002). https://doi.org/10.1007/s00030-002-8123-z

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  • DOI: https://doi.org/10.1007/s00030-002-8123-z

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