Abstract
The paper deals with solutions of nonlinear heat and Navier–Stokes equations in the context of Besov and Triebel–Lizorkin spaces \(B_{p,q}^s(\mathbb {R}^{n})\) and \(F_{p,q}^s(\mathbb {R}^{n})\) where \(1\le p,q \le \infty \) and \(-1+n/p<s<n/p\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Browder, F.E.: Nonlinear equations of evolution. Ann. Math. 80, 485–523 (1964)
Cannone, M.: Harmonic analysis tool for solving the incompressible Navier–Stokes equations. In: Friedlander, S.J., Serre, D. (eds.) Handbook of Mathematical Fluid Dynamics, vol. III, pp. 161–244. North Holland, Amsterdam (2004)
Fujita, H., Kato, T.: On the Navier–Stokes initial value problem. I. Arch. Rational Mech. Anal. 16, 269–315 (1964)
Kato, T.: Nonlinear evolution equations in Banach spaces. In: Proceedings of the Symposium on Applied Mathematics, vol. 17, pp. 50–67. Am. Math. Soc. (1965)
Kato, T.: Strong \(L^p\)-solutions of the Navier–Stokes equation in \(\mathbb{R}^n\), with applications to weak solutions. Math. Z. 187, 471–480 (1984)
Lemarié-Rieusset, P.G.: Recent developements in the Navier–Stokes problem. In: CRC Research Notes in Math., vol. 431, pp. 269–315. Chapman & Hall, Boca Raton (2002)
Miao, C., Yuan, B., Zhang, B.: Well-posedness of the Cauchy problem for the fractional power dissipative equations. Nonlinear Anal. Theory Methods Appl. 68, 461–484 (2008)
Sickel, W., Triebel, H.: Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^{s}\) and \(F_{pq}^s\) type. Z. Anal. Anwend. 14, 105–140 (1995)
Triebel, H.: Theory of Functions Spaces. Birkhäuser, Basel (1983)
Triebel, H.: Theory of Functions Spaces II. Birkhäuser, Basel (1992)
Triebel, H.: Higher Analysis. Barth, Leipzig (1992)
Triebel, H.: Theory of Functions Spaces III. Birkhäuser, Basel (2006)
Triebel, H.: Local functions spaces, heat and Navier–Stokes equations. In: EMS Tracts in Mathematics, vol. 20 (2013)
Acknowledgments
I would like to thank Hans-Jürgen Schmeißer and Hans Triebel for useful comments and suggestions. Furthermore I wish to thank the referee for careful reading and valuable comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baaske, F. Heat and Navier–Stokes equations in supercritical function spaces. Rev Mat Complut 28, 281–301 (2015). https://doi.org/10.1007/s13163-014-0166-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13163-014-0166-2