The Fractional Navier-Stokes Equations with delay conditions
Abstract
Throught this paper,we study the cauchy problem for the conformable fractional Navier-Stokes Equations (FNSE) with finite delay external forces, contains some hereditary features, on a bounded domain. We prove that there exist a unique local mild solutions for the initial datum, by using semigroup theory, conformable fractional calculus and Banach contraction theorem.With more conditions on delay external forces we establish the globality and continuation of the mild solutions.
Downloads
References
T. Abdeljawad, On conformable fractional calculus, Journalof Computational and Applied Mathematics, 279, 57-66, (2015).
T. Caraballo and J. Real, Navier-Stokes equations with delays. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 457(2014), 2441-2453, (2001)..
P. M. Carvalho Neto, G.Planas, Mild solutions to the time fractional Navier-Stokes equations in RN, J. Differ. Equ. 259(7), 2948-2980 (2015)
H.Fujita and T. Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16, 269-315, (1964).
M. Hannabou, K. Hilal, A.Kajouni, Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems, Journal of Mathematics,(2020)
B. Hendriya Guswanto, On the properties of solution operators of fractional evolution equations, J. Fract. Calc. Appl. 6(1), 131-159, (2015)
T. Kato and H. Fujita, On the nonstationary Navier-Stokes system, Rend. Semin. Mat. Univ. Padova 32, 243-260, (1962).
R. Khalil, M. Al Horani, A. Yousef, and M.Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70, (2014).
J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l’hydrodynamique, J. Math. Pures Appl. 12, 1-82, (1933).
G. M. Lorenzi, A.Lunardi and D.Pallara, Analytic semigroups and reaction–diffusion equations. In Internate seminar 2004-2005, http://www.math.unipr.it/˜lunardi/LectureNotes/I-Sem2005.pdf.
A. Pazy, Semigroups Of Linear operators and Applications to partial differential equations, Appl.Math. Sci. 44, Springer-Verlag, New York, 1983.
H. Sohr, The Navier-Stokes equations: An elementary functional analytic approach, Modern Birkhäuser Classics. Birkhäuser, Springer Basel AG, Basel, 2001.
Y. Wang and T. Liang, Mild solutions to the time fractional Navier-Stokes delay differential inclusions, Discr. Contin. Dyn. Syst. Ser. B. 24.8, 3713-3740 (2019).
Y. Zhou and L. Peng, On the time-fractional Navier-Stokes equations, Comput. Math. Appl. 73.6, 874-891 (2017).
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
