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Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure

  • * Corresponding author: Kyungkeun Kang

    * Corresponding author: Kyungkeun Kang

Bum Ja Jin's work is supported by NRF-2014R1A1A3A04049515 and Kyungkeun Kang's work was partially supported by NRF-2014R1A2A1A11051161 and NRF20151009350

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  • We prove a Caccioppoli type inequality for the solution of a parabolic system related to the nonlinear Stokes problem. Using the method of Caccioppoli type inequality, we also establish the existence of weak solutions satisfying a local energy inequality without pressure for the non-Newtonian Navier-Stokes equations.

    Mathematics Subject Classification: Primary: 76A05, 76D03; Secondary: 76D05, 76D07.


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