• Previous Article
    Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems
  • CPAA Home
  • This Issue
  • Next Article
    Bounds on Sobolev norms for the defocusing nonlinear Schrödinger equation on general flat tori
March  2010, 9(2): 493-537. doi: 10.3934/cpaa.2010.9.493

Stokes-Brinkman transmission problems on Lipschitz and $C^1$ domains in Riemannian manifolds

1. 

Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084 Cluj-Napoca, Romania, Romania

2. 

Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Received  February 2009 Revised  September 2009 Published  December 2009

The purpose of this paper is to treat some transmission problems for the Stokes-Brinkman-coupled system on Lipschitz or $C^1$ domains in Riemannian manifolds, by using the method of boundary integral equations.
Citation: Mirela Kohr, Cornel Pintea, Wolfgang L. Wendland. Stokes-Brinkman transmission problems on Lipschitz and $C^1$ domains in Riemannian manifolds. Communications on Pure and Applied Analysis, 2010, 9 (2) : 493-537. doi: 10.3934/cpaa.2010.9.493
[1]

Mirela Kohr, Cornel Pintea, Wolfgang L. Wendland. Dirichlet - transmission problems for general Brinkman operators on Lipschitz and $C^1$ domains in Riemannian manifolds. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 999-1018. doi: 10.3934/dcdsb.2011.15.999

[2]

Mirela Kohr, Cornel Pintea, Wolfgang L. Wendland. Neumann-transmission problems for pseudodifferential Brinkman operators on Lipschitz domains in compact Riemannian manifolds. Communications on Pure and Applied Analysis, 2014, 13 (1) : 175-202. doi: 10.3934/cpaa.2014.13.175

[3]

Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang. Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 363-386. doi: 10.3934/dcdsb.2018084

[4]

Van Duong Dinh. On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1127-1143. doi: 10.3934/dcds.2018047

[5]

Wei Yan, Yimin Zhang, Yongsheng Li, Jinqiao Duan. Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 5825-5849. doi: 10.3934/dcds.2021097

[6]

Erwann Delay, Pieralberto Sicbaldi. Extremal domains for the first eigenvalue in a general compact Riemannian manifold. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5799-5825. doi: 10.3934/dcds.2015.35.5799

[7]

Beom-Seok Han, Kyeong-Hun Kim, Daehan Park. A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on $ C^{1} $ domains. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3415-3445. doi: 10.3934/dcds.2021002

[8]

Shengbing Deng, Zied Khemiri, Fethi Mahmoudi. On spike solutions for a singularly perturbed problem in a compact riemannian manifold. Communications on Pure and Applied Analysis, 2018, 17 (5) : 2063-2084. doi: 10.3934/cpaa.2018098

[9]

Anna Maria Candela, J.L. Flores, M. Sánchez. A quadratic Bolza-type problem in a non-complete Riemannian manifold. Conference Publications, 2003, 2003 (Special) : 173-181. doi: 10.3934/proc.2003.2003.173

[10]

Haruki Umakoshi. A semilinear heat equation with initial data in negative Sobolev spaces. Discrete and Continuous Dynamical Systems - S, 2021, 14 (2) : 745-767. doi: 10.3934/dcdss.2020365

[11]

Ioannis Markou. Hydrodynamic limit for a Fokker-Planck equation with coefficients in Sobolev spaces. Networks and Heterogeneous Media, 2017, 12 (4) : 683-705. doi: 10.3934/nhm.2017028

[12]

Matthias Geissert, Horst Heck, Matthias Hieber, Okihiro Sawada. Remarks on the $L^p$-approach to the Stokes equation on unbounded domains. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 291-297. doi: 10.3934/dcdss.2010.3.291

[13]

Lukáš Poul. Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains. Conference Publications, 2007, 2007 (Special) : 834-843. doi: 10.3934/proc.2007.2007.834

[14]

Sylvie Monniaux. Various boundary conditions for Navier-Stokes equations in bounded Lipschitz domains. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1355-1369. doi: 10.3934/dcdss.2013.6.1355

[15]

Bojing Shi. $ W^{1, p} $ estimates for elliptic problems with drift terms in Lipschitz domains. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 537-553. doi: 10.3934/dcds.2021127

[16]

Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems and Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159

[17]

Emanuela R. S. Coelho, Valéria N. Domingos Cavalcanti, Vinicius A. Peralta. Exponential stability for a transmission problem of a nonlinear viscoelastic wave equation. Communications on Pure and Applied Analysis, 2021, 20 (5) : 1987-2020. doi: 10.3934/cpaa.2021055

[18]

Zhiling Guo, Shugen Chai. Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022001

[19]

Laurent Amour, Jérémy Faupin. Inverse spectral results in Sobolev spaces for the AKNS operator with partial informations on the potentials. Inverse Problems and Imaging, 2013, 7 (4) : 1115-1122. doi: 10.3934/ipi.2013.7.1115

[20]

Mohamed Jleli, Bessem Samet. Instantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds. Communications on Pure and Applied Analysis, 2022, 21 (6) : 2065-2078. doi: 10.3934/cpaa.2022036

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (106)
  • HTML views (0)
  • Cited by (12)

[Back to Top]