Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
Rendiconti del Seminario Matematico della Università di Padova, Tome 125 (2011), pp. 51-70.
@article{RSMUP_2011__125__51_0,
     author = {Farwig, R. and Kozono, H. and Sohr, H.},
     title = {Global weak solutions of the {Navier-Stokes} equations with nonhomogeneous boundary data and divergence},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {51--70},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {125},
     year = {2011},
     mrnumber = {2866119},
     zbl = {1236.35103},
     language = {en},
     url = {http://archive.numdam.org/item/RSMUP_2011__125__51_0/}
}
TY  - JOUR
AU  - Farwig, R.
AU  - Kozono, H.
AU  - Sohr, H.
TI  - Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2011
SP  - 51
EP  - 70
VL  - 125
PB  - Seminario Matematico of the University of Padua
UR  - http://archive.numdam.org/item/RSMUP_2011__125__51_0/
LA  - en
ID  - RSMUP_2011__125__51_0
ER  - 
%0 Journal Article
%A Farwig, R.
%A Kozono, H.
%A Sohr, H.
%T Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2011
%P 51-70
%V 125
%I Seminario Matematico of the University of Padua
%U http://archive.numdam.org/item/RSMUP_2011__125__51_0/
%G en
%F RSMUP_2011__125__51_0
Farwig, R.; Kozono, H.; Sohr, H. Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence. Rendiconti del Seminario Matematico della Università di Padova, Tome 125 (2011), pp. 51-70. http://archive.numdam.org/item/RSMUP_2011__125__51_0/

[1] H. Amann, On the strong solvability of the Navier-Stokes equations. J. Math. Fluid Mech., 2 (2000), pp. 16-98. | MR | Zbl

[2] H. Amann, Navier-Stokes equations with nonhomogeneous Dirichlet data, J. Nonlinear Math. Phys., 10, Suppl. 1 (2003), pp. 1-11. | MR

[3] R. Farwig - G. P. Galdi - H. Sohr, A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data, J. Math. Fluid Mech., 8 (2006), pp. 423-444. | MR | Zbl

[4] R. Farwig - H. Kozono - H. Sohr, Global weak solutions of the Navier-Stokes system with nonzero boundary conditions. Funkcial. Ekvac., 53 (2010), pp. 231-247. | MR

[5] R. Farwig - H. Kozono - H. Sohr, Global Leray-Hopf weak solutions of the Navier-Stokes equations with nonzero time-dependent boundary values. Progress Nonl. Differential Equations Appl., Birkhäuser-Verlag Basel, 60 (2011), pp. 211-232.

[6] A. V. Fursikov - M. D. Gunzburger - L. S. Hou, Inhomogeneous boundary value problems for the three-dimensional evolutionary Navier-Stokes equations. J. Math. Fluid Mech., 4 (2002), pp. 45-75. | MR | Zbl

[7] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I, Springer Verlag, New York, 1994. | MR | Zbl

[8] Y. Giga, Analyticity of the semigroup generated by the Stokes operator in L r -spaces. Math. Z., 178 (1981), pp. 297-329. | MR | Zbl

[9] Y. Giga - H. Sohr, Abstract L p estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains. J. Funct. Anal., 102 (1991), pp. 72-94. | MR | Zbl

[10] G. Grubb, Nonhomogeneous Dirichlet Navier-Stokes problems in low regularity L p Sobolev spaces. J. Math. Fluid Mech., 3 (2001), pp. 57-81. | MR | Zbl

[11] J. G. Heywood, The Navier-Stokes Equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J., 29 (1980), pp. 639-681. | MR | Zbl

[12] E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr., 4 (1950), pp. 213-231. | MR | Zbl

[13] O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York, 1969. | MR | Zbl

[14] J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math., 63 (1934), pp. 193-248. | JFM | MR

[15] J. P. Raymond, Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 24 (2007), pp. 921-951. | MR | Zbl

[16] H. Sohr, The Navier-Stokes Equations. Birkhäuser Verlag, Basel, 2001. | Zbl

[17] V. A. Solonnikov, Estimates for solutions of nonstationary Navier-Stokes equations. J. Soviet Math., 8 (1977), pp. 467-529. | Zbl

[18] R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam, 1977. | MR | Zbl