Note on the fast decay property of steady Navier–Stokes flows in the whole space

References

[1] W. Borchers and T. Miyakawa, On stability of exterior stationary Navier–Stokes flows, Acta Math. 174 (1995), no. 2, 311–382. 10.1007/BF02392469Suche in Google Scholar

[2] J. Frehse and M. Růžička, Weighted estimates for the stationary Navier–Stokes equations, Mathematical Theory in Fluid Mechanics (Paseky 1995), Pitman Res. Notes Math. Ser. 354, Longman, Harlow, (1996), 1–29. 10.1007/BF00995129Suche in Google Scholar

[3] H. Fujita, On the existence and regularity of the steady-state solutions of the Navier–Stokes theorem, J. Fac. Sci. Univ. Tokyo Sect. I 9 (1961), 59–102. Suche in Google Scholar

[4] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations. Vol. I: Linearized Steady Problems, Vol. II: Nonlinear Steady Problems, Springer Tracts Natural Philos. 38, Springer, New York, 1994. Suche in Google Scholar

[5] G. P. Galdi and C. G. Simader, New estimates for the steady-state Stokes problem in exterior domains with applications to the Navier–Stokes problem, Differential Integral Equations 7 (1994), no. 3–4, 847–861. 10.57262/die/1370267709Suche in Google Scholar

[6] H. Kozono and H. Sohr, On stationary Navier–Stokes equations in unbounded domains, Ric. Mat. 42 (1993), no. 1, 69–86. Suche in Google Scholar

[7] H. Kozono, H. Sohr and M. Yamazaki, Representation formula, net force and energy relation to the stationary Navier–Stokes equations in 3-dimensional exterior domains, Kyushu J. Math. 51 (1997), no. 1, 239–260. 10.2206/kyushujm.51.239Suche in Google Scholar

[8] H. Kozono and M. Yamazaki, Uniqueness criterion of weak solutions to the stationary Navier–Stokes equations in exterior domains, Nonlinear Anal. 38 (1999), no. 8, 959–970. 10.1016/S0362-546X(98)00145-XSuche in Google Scholar

[9] J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique, J. Math. Pures Appl. (9) 12 (1933), 1–82. Suche in Google Scholar

[10] T. Miyakawa, On uniqueness of steady Navier–Stokes flows in an exterior domain, Adv. Math. Sci. Appl. 5 (1995), no. 2, 411–420. Suche in Google Scholar

[11] T. Miyakawa, Hardy spaces of solenoidal vector fields, with applications to the Navier–Stokes equations, Kyushu J. Math. 50 (1996), no. 1, 1–64. 10.2206/kyushujm.50.1Suche in Google Scholar

[12] T. Miyakawa, On stationary incompressible Navier–Stokes flows with fast decay and the vanishing flux condition, Topics in Nonlinear Analysis, Progr. Nonlinear Differential Equations Appl. 35, Birkhäuser, Basel (1999), 535–552. 10.1007/978-3-0348-8765-6_22Suche in Google Scholar

[13] T. Nakatsuka, Uniqueness of steady Navier–Stokes flows in exterior domains, Funkcial. Ekvac. 56 (2013), no. 2, 323–337. 10.1619/fesi.56.323Suche in Google Scholar

[14] A. Novotný and M. Padula, Note on decay of solutions of steady Navier–Stokes equations in 3-D exterior domains, Differential Integral Equations 8 (1995), no. 7, 1833–1842. 10.57262/die/1368397761Suche in Google Scholar

[15] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Ser. 43, Princeton University Press, Princeton, 1993. 10.1515/9781400883929Suche in Google Scholar