A moving boundary problem for periodic Stokesian Hele-Shaw flows

Interfaces and Free Boundaries

Volumn 11, Issue 1, 2009, Pages 119-137

  Escher, Joachim ^a   Matioc, Bogdan Vasile ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Hele Shaw flow; Non Newtonian fluid; Nonlinear parabolic equation; Quasilinear elliptic equation

Indexed keywords

EID: 73949124799     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/205     Document Type: Article

References (11)

1. AMANN, H. Linear and Quasilinear Parabolic Problems. Volume I, Birkhäuser, Basel (1995). Zbl 0819.35001 MR 1345385
2. ARENDT, W., & BU, S. Operator-valued Fourier multipliers on periodic Besov spaces and applications. Proc. Edinburgh Math. Soc. 47 (2004), 15-33. Zbl 1083.42009 MR 2064734
3. ESCHER, J. On moving boundaries in deformable media. Adv. Math. Sci. Appl. 7 (1997), 275-316. Zbl 0884.35174 MR 1454668
4. ESCHER, J., & PROKERT, G. Stability of the equilibria for spatially periodic flows in porous media. Nonlinear Anal. 45 (2001), 1061-1080. Zbl 0986.35017 MR 1846423
5. ESCHER, J., & SIMONETT, G. Maximal regularity for a free boundary problem. Nonlinear Differential Equations Appl. 2 (1991), 463-510. Zbl 0842.35083 MR 1356871
6. ESCHER, J., & SIMONETT, G. Analyticity of the interface in a free boundary problem, Math. Ann. 305 (1996), 439-459. Zbl 0857.76086 MR 1397432 (Pubitemid 126338933)
7. ESCHER, J., & SIMONETT, G. Classical solutions of multidimensional Hele-Shaw models. SIAM J. Math. Anal. 28 (1997), 1028-1047. Zbl 0888.35142 MR 1466667
8. GILBARG, D., & TRUDINGER, N. S. Elliptic Partial Differential Equations of Second Order. Springer, New York (1977). Zbl 0361.35003 MR 0473443
9. KONDIC, L., PALFFY-MAHORNY, P., & SHELLEY, M. J. Models of non-Newtonian Hele-Shaw flow. Phys. Rev. E 54 (1996), R4536-R4539.
10. LUNARDI, A. Analytic Semigroups and Optimal Regularity in Parabolic Problems. Birkhäuser, Basel (1995). Zbl 0816.35001 MR 1329547
11. SCHMEISSER, H.-J., & TRIEBEL, H. Topics in Fourier Analysis and Function Spaces. Wiley, New York (1987). Zbl 0661.46025 MR 0891189