A well-posed problem for the exterior Stokes equations in two and three dimensions

作者: Vivette Girault , Adelia Sequeira

DOI: 10.1007/BF00376137

关键词:

摘要: This paper treats the Stokes problem in exterior Lipschitz-continuous domains of ℝ2 and ℝ3. Using weighted Sobolev spaces Hanouzet (in ℝ3) Giroire ℝ2), we establish inf-sup condition between velocity pressure spaces. fundamental result shows that variational is well-posed those In last paragraph, obtain additional regularity solution when data are smoother.

参考文章(24)
Hermann Sohr, Werner Varnhorn, On decay properties of the Stokes equations in exterior domains The Navier-Stokes Equations Theory and Numerical Methods. pp. 134- 151 ,(1990) , 10.1007/BFB0086064
Lamberto Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes Rendiconti del Seminario Matematico della Università di Padova. ,vol. 31, pp. 308- 340 ,(1961)
F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique. ,vol. 8, pp. 129- 151 ,(1974) , 10.1051/M2AN/197408R201291
Chun-Ming Ma, On square-summability and uniqueness questions concerning non-stationary stokes flow in an exterior domain Archive for Rational Mechanics and Analysis. ,vol. 71, pp. 99- 112 ,(1979) , 10.1007/BF00248723
Donald R. Smith, Estimates at infinity for stationary solutions of the Navier-Stokes equations in two dimensions Archive for Rational Mechanics and Analysis. ,vol. 20, pp. 341- 372 ,(1965) , 10.1007/BF00282357
Georges H. Guirguis, On the existence, uniqueness and regularity of the exterior stokes problem in R3 Communications in Partial Differential Equations. ,vol. 11, pp. 567- 594 ,(1986) , 10.1080/03605308608820437
Adélia Sequeira, Lisboa, Palaiseau, J. C. Nedelec, On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady stokes problem Mathematical Methods in The Applied Sciences. ,vol. 8, pp. 117- 133 ,(1986) , 10.1002/MMA.1670080109
Jean Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace Acta Mathematica. ,vol. 63, pp. 193- 248 ,(1934) , 10.1007/BF02547354