Asymptotic expansion of the solution of a transmission problem for the Stokes system with a small boundary perturbation for an inclusion

References

• Ammari H, Garapon P, Kang H, et al. A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements. Quart Appl Math. 2008;66(1):139–175. doi: 10.1090/S0033-569X-07-01089-8
   Web of Science ®Google Scholar
• Boyer F, Fabrie P. Mathematical tools for the study of the incompressible Navier–Stokes equations and related models. Applied Mathematical Sciences. vol. 183. Springer; 2013.
   Google Scholar
• Ladyzhenskaya AO. The mathematical theory of viscous incompressible flow. New York: Gordon and Breach Science Publishers; 1967.
   Google Scholar
• Temam R. Navier–Stokes equations theory and numerical analysis. Amsterdam, New York: North-Holland Publishing Company; 1977.
   Google Scholar
• Luong THC, Daveau C. Asymptotic formula for the solution of the Stokes problem with a small perturbation of the domain in two and three dimensions. Complex Var Elliptic. 2014;59(9):1269–1282. doi: 10.1080/17476933.2013.831846
   Web of Science ®Google Scholar
• Daveau C, Khelifi A, Balloumi I. Asymptotic behaviors for eigenvalues and eigenfunctions associated to Stokes operator in the presence of small boundary perturbations. Math Phys Anal Geom. 2017;20:13. doi: 10.1007/s11040-017-9243-3
   Web of Science ®Google Scholar
• Zribi H. Asymptotic expansions for currents caused by small interface changes of an electromagnetic inclusion. Appl Anal. 1984;92:172–190. doi: 10.1080/00036811.2011.601601
   Google Scholar
• Ammari H, Kang H, Lee H. Layer potential techniques in spectral analysis. Providence: American Mathematical Society; 2009.
   Google Scholar
• Varhorn W. An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions. Manuscripta Math. 1991;70(4):339–361. doi: 10.1007/BF02568383
   Web of Science ®Google Scholar
• Varnhorn W. Boundary value problems and integral equations for the Stokes resolvent in bounded and exterior domains of Rn. Theory of the Navier-Stokes Equations 1998;206–224. DOI:10.1142/9789812816740_0016.
   Google Scholar
• Varnhorn W. The boundary value problems of the Stokes resolvent equations in n dimensions. Math Nachr. 2004;269–270:210–230. doi: 10.1002/mana.200310173
   Web of Science ®Google Scholar
• Verchota GC. Layer potentials and regularity for Laplace's equation in Lipschitz domains. J Funct Anal. 1984;59:572–611. doi: 10.1016/0022-1236(84)90066-1
   Web of Science ®Google Scholar
• Escauriaza L, Fabes E, Verchota G. On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries. Proc Amer Math Soc. 1992;115:1069–1076. doi: 10.1090/S0002-9939-1992-1092919-1
   Web of Science ®Google Scholar
• Escauriaza L, Mitrea M. Transmission problems and spectral theory for singular integral operators on Lipschitz domains. J Funct Anal. 2004;216:141–171. doi: 10.1016/j.jfa.2003.12.005
   Web of Science ®Google Scholar
• Escauriaza L, Seo JK. Regularity properties of solutions to transmission problems. Trans Amer Math Soc. 1993;338:405–430. doi: 10.1090/S0002-9947-1993-1149120-8
   Web of Science ®Google Scholar
• Kohr M. An indirect boundary integral method for an oscillatory Stokes flow problem. IJMMS. 2003;47:2916–2976.
   Google Scholar
• Kohr M. The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn. Arch Mech. 2007;59(3):283–304. Warszawa.
   Web of Science ®Google Scholar
• Medková D. Integral representation of a solution of the Neumann problem for the Stokes system. Kragujivac J Math. 2015;39:53–71. doi: 10.5937/KgJMath1501053M
   Google Scholar
• Mitrea M, Wright M. Boundary value problems for the Stokes system in arbitrary Lipschitz domains. In: Heywood JG, Masuda K, Rautmann R, et al., editors. Theory of the Navier-Stokes Equations. Singapore: World Scientific Publishing; 1998. p. 206–224.
   Google Scholar
• Khelifi A, Zribi H. Boundary voltage perturbations resulting from small surface changes of a conductivity inclusion. Appl Anal. 2014;93(1):46–64. doi: 10.1080/00036811.2012.755734
   Web of Science ®Google Scholar
• Coifman RR, Goldberg M, Hrycak T, et al. An improved operator expansion algorithm for direct and inverse scattering computations. Wave Random Media. 1999;9:441–457. doi: 10.1088/0959-7174/9/3/311
   Google Scholar
• Kress R. Linear integral equations. 3rd ed. Vol. 82. Berlin: Springer; 2014. (Applied mathematical sciences).
   Google Scholar
• Varnhorn W. The Stokes equations. Berlin: Akademie Verlag; 1994.
   Google Scholar