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

Bum Ja Jin; Kyungkeun Kang

doi:10.3934/dcds.2017207

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

Bum Ja Jin, Kyungkeun Kang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

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.

Original language	English
Pages (from-to)	4815-4834
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	37
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2017207
Publication status	Published - 2017 Sept

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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title = "Caccioppoli type inequality for non-Newtonian stokes system and a local energy inequality of non-Newtonian navier-stokes equations without pressure",

abstract = "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.",

author = "Jin, {Bum Ja} and Kyungkeun Kang",

year = "2017",

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doi = "10.3934/dcds.2017207",

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N2 - 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.

AB - 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.

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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

Abstract

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