American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Local existence theorems with unbounded set of input data and unboundedness of stable invariant manifolds for 3D Navier-Stokes equations
  • DCDS-S Home
  • This Issue
  • Next Article
    A representation formula for linearized stationary incompressible viscous flows around rotating and translating bodies
June  2010, 3(2): 255-268. doi: 10.3934/dcdss.2010.3.255

An existence result for non-Newtonian fluids in non-regular domains

Lars Diening 1, and  Michael Růžička 1,

1. 

Universität Freiburg, Mathematisches Institut, Eckerstr. 1, D-79104 Freiburg, Germany, Germany

Received  May 2009 Published  April 2010

We show the existence of weak solutions to the steady system describing the motion of certain non-Newtonian fluids in non-regular domains. This generalizes previous results for Lipschitz continuous domains. In the proof we combine a localization of the Lipschitz truncation method with a domain decomposition theorem, which enables to extend results known for nice domains to John domains.
Keywords: divergence equation, Lipschitz truncation method, theorem of de Rham., domain decomposition, non-Newtonian fluids, John domains, Korn's inequality, electrorheological fluids, Lebesgue and Sobolev spaces with variable exponents.
Mathematics Subject Classification: 35Q35, 35D05, 26D10, 46E30, 35B4.
Citation: Lars Diening, Michael Růžička. An existence result for non-Newtonian fluids in non-regular domains. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 255-268. doi: 10.3934/dcdss.2010.3.255
[1]

Jan Sokołowski, Jan Stebel. Shape optimization for non-Newtonian fluids in time-dependent domains. Evolution Equations & Control Theory, 2014, 3 (2) : 331-348. doi: 10.3934/eect.2014.3.331
[2]

Aneta Wróblewska-Kamińska. Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces. Discrete & Continuous Dynamical Systems, 2013, 33 (6) : 2565-2592. doi: 10.3934/dcds.2013.33.2565
[3]

Pitágoras Pinheiro de Carvalho, Juan Límaco, Denilson Menezes, Yuri Thamsten. Local null controllability of a class of non-Newtonian incompressible viscous fluids. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021043
[4]

Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037
[5]

Xin Liu, Yongjin Lu, Xin-Guang Yang. Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids. Evolution Equations & Control Theory, 2021, 10 (2) : 365-384. doi: 10.3934/eect.2020071
[6]

Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096
[7]

W. G. Litvinov, R. H.W. Hoppe. Coupled problems on stationary non-isothermal flow of electrorheological fluids. Communications on Pure & Applied Analysis, 2005, 4 (4) : 779-803. doi: 10.3934/cpaa.2005.4.779
[8]

Bum Ja Jin, Kyungkeun Kang. Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure. Discrete & Continuous Dynamical Systems, 2017, 37 (9) : 4815-4834. doi: 10.3934/dcds.2017207
[9]

Luigi Fontana, Steven G. Krantz and Marco M. Peloso. Hodge theory in the Sobolev topology for the de Rham complex on a smoothly bounded domain in Euclidean space. Electronic Research Announcements, 1995, 1: 103-107.

[10]

Gang Cai, Yekini Shehu, Olaniyi S. Iyiola. Inertial Tseng's extragradient method for solving variational inequality problems of pseudo-monotone and non-Lipschitz operators. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021095
[11]

Emil Novruzov. On existence and nonexistence of the positive solutions of non-newtonian filtration equation. Communications on Pure & Applied Analysis, 2011, 10 (2) : 719-730. doi: 10.3934/cpaa.2011.10.719
[12]

Jong Yeoul Park, Jae Ug Jeong. Pullback attractors for a $2D$-non-autonomous incompressible non-Newtonian fluid with variable delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2687-2702. doi: 10.3934/dcdsb.2016068
[13]

Jiahui Chen, Rundong Zhao, Yiying Tong, Guo-Wei Wei. Evolutionary de Rham-Hodge method. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3785-3821. doi: 10.3934/dcdsb.2020257
[14]

W. G. Litvinov. Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary. Communications on Pure & Applied Analysis, 2007, 6 (1) : 247-277. doi: 10.3934/cpaa.2007.6.247
[15]

Zhong Tan, Jianfeng Zhou. Higher integrability of weak solution of a nonlinear problem arising in the electrorheological fluids. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1335-1350. doi: 10.3934/cpaa.2016.15.1335
[16]

Aneta Wróblewska-Kamińska. Local pressure methods in Orlicz spaces for the motion of rigid bodies in a non-Newtonian fluid with general growth conditions. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1417-1425. doi: 10.3934/dcdss.2013.6.1417
[17]

Hailong Ye, Jingxue Yin. Instantaneous shrinking and extinction for a non-Newtonian polytropic filtration equation with orientated convection. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1743-1755. doi: 10.3934/dcdsb.2017083
[18]

Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011
[19]

Jingxue Yin, Chunhua Jin. Critical exponents and traveling wavefronts of a degenerate-singular parabolic equation in non-divergence form. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 213-227. doi: 10.3934/dcdsb.2010.13.213
[20]

Julii A. Dubinskii. Complex Neumann type boundary problem and decomposition of Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 201-210. doi: 10.3934/dcds.2004.10.201

2020 Impact Factor: 2.425

Tools

Metrics

  • PDF downloads (96)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences