Global weak solutions for an incompressible charged fluid with multi-scale couplings: Initial-boundary-value problem

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 12, 2009, Pages

  Jerome, Joseph W ^a   Sacco, Riccardo ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Initial boundary problem for hybrid systems; Navier Stokes; Poisson Nernst Planck; Rothe's method; Slip boundary condition

Indexed keywords

ANALYTICAL APPROACH; CAUCHY PROBLEMS; CHARGE TRANSPORT; CHARGED FLUIDS; EVOLUTION EQUATIONS; GLOBAL WEAK SOLUTION; HYBRID DEVICES; INITIAL BOUNDARY PROBLEMS; INITIAL-BOUNDARY PROBLEM FOR HYBRID SYSTEMS; LAB-ON-CHIP TECHNOLOGY; LOCAL EXISTENCE; MICRO-FLUIDIC DEVICES; MOVING MEDIUM; MULTISCALES; NAVIER STOKES; NEURONAL CELL; SLIP BOUNDARY CONDITIONS; STOKES MODEL; TRANSPORT THEORY;

BOUNDARY CONDITIONS; DIELECTRIC PROPERTIES; ELECTRIC GROUNDING; HYBRID COMPUTERS; HYBRID SYSTEMS; INCOMPRESSIBLE FLOW; INITIAL VALUE PROBLEMS; NAVIER STOKES EQUATIONS; POISSON DISTRIBUTION; STATISTICAL MECHANICS; TISSUE ENGINEERING;

POISSON EQUATION;

EID: 72149102698     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.05.047     Document Type: Article

References (26)

1. Fromherz P. Neuroelectronics interfacing: Semiconductor chips with ion channels, cells, and brain. In: Weise R. (Ed). Nanoelectronics and Information Technology (2003), Wiley-VCH, Berlin 781-810
2. Offenhäuser A., Rühe J., and Knoll W. Neuronal cells cultured on modified microelectronic device structures. J. Vac. Sci. Technol. A 13 5 (1995) 2606-2612
3. Raimondi M.T., Boschetti F., Migliavacca F., Cioffi M., and Dubini G. Micro-fluid dynamics in three-dimensional engineered cell systems in bioreactors. In: Ashammakhi N., and Reis R.L. (Eds). Topics in Tissue Engineering, vol. 2 (2005) (Chapter 9)
4. Cioffi M., Boschetti F., Raimondi M.T., and Dubini G. Modeling evaluation of the fluid-dynamic microenvironment in tissue-engineered constructs: A micro-CT based model. Biotechnol. Bioeng. 93 (2006) 500-510
5. Choi H.-W., and Paraschivoiu M. Advanced hybrid-flux approach for output bounds of electro-osmotic flows: Adaptive refinement and direct equilibrating strategies. Microfluidics Nanofluidics 2 (2006) 154-170
6. Hu Y., Lee J., Werner C., and Li D. Electrokinetically controlled concentration gradients in micro-chambers in microfluidic systems. Microfluidics Nanofluidics 2 (2006) 141-153
7. Longaretti M., Marino G., Chini B., Jerome J., and Sacco R. Computational models in nano-bio-electronics: Simulation of ionic transport in voltage operated channels. J. Nanosci. Nanotechnology 8 (2008) 3686-3694
8. Longaretti M., Chini B., Jerome J., and Sacco R. Electrochemical modeling and characterization of voltage operated channels in nano-bio-electronics. Sensor Letters 6 (2008) 49-56
9. Longaretti M., Chini B., Jerome J., and Sacco R. Computational modeling and simulation of complex systems in bio-electronics. J. Comput. Electron. 7 (2008) 10-13
10. Rubinstein I. Electro-diffusion of Ions (1990), SIAM
11. Jerome J.W. An analytical approach to charge transport in a moving medium. Transport Theory Statist. Phys. 31 (2002) 333-366
12. Avalos G., and Triggiani R. Mathematical analysis of PDE systems which govern fluid-structure interactive phenomena. Bol. Soc. Parana. Mat. (3) 25 1-2 (2007) 17-36
13. Mitrea M., and Monniaux S. The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains. J. Funct. Anal. 254 (2008) 1522-1574
14. Saidi F. On the Navier-Stokes equation with slip boundary conditions of friction type. Math. Model. Anal. 12 (2007) 389-398
15. Gala S. Regularity criterion on weak solutions to the Navier-Stokes equations. J. Korean Math. Soc. 45 (2008) 537-558
16. Temam R. Navier-Stokes Equations. 3rd. rev. ed. (1984), North-Holland Publishers
17. Jerome J.W. Approximation of Nonlinear Evolution Systems (1983), Academic Press
18. Brezis H. Équations et inquations non linaires dans les espaces vectoriels en dualité. Ann. Inst. Fourier (Grenoble) 18 (1968) 115-175 (in French)
19. Jerome J.W. A trapping principle and convergence result for finite element approximate solutions of steady reaction diffusion systems. Numer. Math. 109 (2008) 121-142
20. Jerome J.W. Evolution systems in semiconductor device modeling: A cyclic uncoupled line analysis for the Gummel map. Math. Methods Appl. Sci. 9 (1987) 455-492
21. Jerome J.W. Analysis of Charge Transport (1996), Springer-Verlag, Berlin Heidelberg
22. Quarteroni A., and Valli A. Domain Decomposition Methods for Partial Differential Equations (1999), Oxford Science Publications, New York
23. Causin P., and Sacco R. A dual-mixed hybrid formulation for fluid mechanics problems: Mathematical analysis and application to semiconductor process technology. Comput. Methods Appl. Mech. Engrg. 192 (2003) 593-612
24. Brezzi F., Marini L.D., Micheletti S., Pietra P., and Sacco R. Stability and error analysis of mixed finite volume methods for advective-diffusive problems. Comput. Math. Appl. 51 (2006) 681-696
25. Chung C.A., Chen C.W., Chen C.P., and Tseung C.S. Enhancement of cell growth in tissue engineering constructs under direct perfusion: Modeling and simulation. Biotechnol. Bioeng. 97 (2007) 1603-1616
26. Cockburn B., Karniadakis G.E., and Shu C.-W. The development of Discontinuous Galerkin methods. In: Cockburn B., Karniadakis G.E., and Shu C.-W. (Eds). Lecture Notes in Computational Science and Engineering vol. 11 (2000), Springer, New York 3-50