ON THE GEVREY REGULARITY OF SOLUTIONS TO THE THREE DIMENSIONAL GENERALIZED NAVIER-STOKES EQUATIONS WITH FRACTIONAL VOIGT REGULARIZATION
Main Article Content
Abstract
In this paper, we study the Gevrey regularity of solutions to the three-dimensional generalized Navier-Stokes equations with fractional Voigt regularization. Our result improves and extends previous ones.
Keywords
Fractional Voigt-regularization, generalized Navier-Stokes equations, fractional Laplacian, Sobolev regularity, Gevrey regularity
Article Details
References
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26, 303-327.
[6] F. John (1982), Partial Differrential Equations, Springer, New York.
[7] V.K. Kalantarov, B. Levant and E.S. Titi (2009), Gevrey Regularity for the Attractor
of the 3D Navier-Stokes-Voight Equations, J. Nonlinear. Sci. 19, 133-152.
[8] A. Larios and E. S. Titi (2010), On the higher-order global regularity of the inviscid
Voigt-regularization of three-dimensional hydrodynamic models, Discrete and
Continuous Dynamical Systems-B, 14(2):603-627.
[9] C.D. Levermore and M. Oliver (1997), Analyticity of solutions for a generalized
Euler equation, J. Differential Equations 133, 321-339.
[10] A.P. Oskolkov (1973), The uniqueness and solvability in the large of boundary value
problems for the equations of motion of aqueous solutions of polymers, Zap. Nauchn.
Sem. Leningrad. Otdel. Math. Inst. Steklov. (LOMI) 38, 98-136.
the 3D Navier-Stokes-Voigt equations, Comput. Math. Appl. 73(4):601-615.
[2] M. Bohm (1992), On Navier-Stokes and Kelvin-Voigt equations in three dimensions
in interpolation spaces, Math. Nachr. 155, 151-165.
[3] Z. Brzezniak, A. Larios, and I. Safarik (2025), Fractional Voigt-Regularization of
the 3D Navier–Stokes and Euler Equations: Global Well-Posedness and Limiting
Behavior, J. Math. Fluid Mech. 27, 45.
[4] Y. Cao, E.M. Lunasin, and E.S. Titi (2006), Global well-posedness of the threedimensional viscous and inviscid simplified Bardina turbulence models, Commun.
Math. Sci. 4, 823-848.
[5] A. Ilyin, V. Kalantarov and S. Zelik (2026), Attractors and their dimensions for the
3D Fractional Navier-Stokes-Voigt Equations, Discrete Contin. Dyn. Syst. Ser. S .
26, 303-327.
[6] F. John (1982), Partial Differrential Equations, Springer, New York.
[7] V.K. Kalantarov, B. Levant and E.S. Titi (2009), Gevrey Regularity for the Attractor
of the 3D Navier-Stokes-Voight Equations, J. Nonlinear. Sci. 19, 133-152.
[8] A. Larios and E. S. Titi (2010), On the higher-order global regularity of the inviscid
Voigt-regularization of three-dimensional hydrodynamic models, Discrete and
Continuous Dynamical Systems-B, 14(2):603-627.
[9] C.D. Levermore and M. Oliver (1997), Analyticity of solutions for a generalized
Euler equation, J. Differential Equations 133, 321-339.
[10] A.P. Oskolkov (1973), The uniqueness and solvability in the large of boundary value
problems for the equations of motion of aqueous solutions of polymers, Zap. Nauchn.
Sem. Leningrad. Otdel. Math. Inst. Steklov. (LOMI) 38, 98-136.