Upper and lower bounds of time decay rate of solutions to a class of incompressible third grade fluid equations

DOI10.1016/j.nonrwa.2013.08.001zbMath1297.35194OpenAlexW2081189146MaRDI QIDQ2253327

Yunyun Liang, Min Zhao, Caidi Zhao

Publication date: 25 July 2014

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2013.08.001

zbMATH Keywords

Fourier splitting methodincompressible third grade fluid equations

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Weak solutions to PDEs (35D30) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Related Items (18)

Upper bound of decay rate for solutions to the Navier-Stokes-Voigt equations in \(\mathbb{R}^3\) ⋮ Asymptotic behavior of weak solutions to the generalized nonlinear partial differential equation model ⋮ Remarks on \(L^{2}\) decay of solutions for the third-grade non-Newtonian fluid flows in \(\mathbb{R}^{3}\) ⋮ Global regularity for MHD Sisko fluid in annular pipe ⋮ The optimal upper and lower bounds of convergence rates for the 3D Navier-Stokes equations under large initial perturbation ⋮ \(L^2\) decay for the 2-D Oldroyd-B model with linear damping stress ⋮ Decay of solution for a 2D irrotational Mindlin-Timoshenko plate system ⋮ A class of three dimensional Cahn-Hilliard equation with nonlinear diffusion ⋮ The unique existence of weak solution and the optimal control for time-fractional third grade fluid system ⋮ Approximation of a class of incompressible third grade fluids equations ⋮ Error estimates for solutions of the semilinear parabolic equation in whole space ⋮ Upper and lower convergence rates for weak solutions of the 3D non-Newtonian flows ⋮ Time decay rate of weak solutions to the generalized MHD equations in \(\mathbb{R}^2\) ⋮ Time decay rates of the micropolar equations with zero angular viscosity ⋮ Long-time behaviors for the Navier-Stokes equations under large initial perturbation ⋮ Decay of solutions to a class of incompressible third grade fluid equations ⋮ Asymptotic behavior of solutions to a class of incompressible third grade fluid equations ⋮ Global well-posedness and large time behavior of epitaxy thin film growth model

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping
• Decay estimates for homogeneous Boussinesq equations in a semi-infinite pipe
• Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations
• Time decay rates of non-Newtonian flows in \(\mathbf {R}^{n}_{+}\)
• Remarks on upper and lower bounds of solutions to the Navier--Stokes equations in \(\mathbb R^{2}\)
• Global existence and uniqueness of solutions for the equations of third grade fluids
• Decay and scattering of solutions for a generalized Boussinesq equation
• \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
• \(L^ 2\) decay for the Navier-Stokes flow in halfspaces
• Existence, regularity, and decay rate of solutions of non-Newtonian flow
• Decay and scattering of small solutions of a generalized Boussinesq equation
• Weak and classical solutions of a family of second grade fluids
• Decay rates for the incompressible Navier-Stokes flows in 3D exterior domains
• \(L^2\) decay for weak solution to equations of non-Newtonian incompressible fluids in the whole space.
• Large time behavior to the system of incompressible non-Newtonian fluids in \(\mathbb{R}^2\)
• Large-time behaviour of solutions to the magneto-hydrodynamics equations
• Remark on the rate of decay of higher order derivatives for solutions to the Navier-Stokes equations in \(\mathbb{R}^n\)
• Global weak solution and large-time behavior for the compressible flow of liquid crystals
• New asymptotic profiles of nonstationary solutions of the Navier-Stokes system
• Decay results of solutions to the incompressible Navier-Stokes flows in a half space
• Decay of weak solutions to the 2D dissipative quasi-geostrophic equation
• On the decay properties of solutions to the non-stationary Navier–Stokes equations in R³
• Algebraic L2 decay for the solution to a class system of non-Newtonian fluid in Rn
• Large time decay and growth for solutions of a viscous Boussinesq system
• Large time behaviour of solutions to the navier-stokes equations
• A solution formula for the Stokes equation in Rn+
• Decay Results for Weak Solutions of the Navier-Stokes Equations on Rⁿ
• Lower Bounds of Rates of Decay for Solutions to the Navier-Stokes Equations
• Large Time Behaviour of Solutions to the Navier-Stokes Equations in H Spaces
• Sharp Rate of Decay of Solutions to 2-Dimensional Navier-Stokes Equations
• On the decay of higher-order norms of the solutions of Navier–Stokes equations
• Asymptotic Behavior of Solutions to Liquid Crystal Systems in ℝ³
• Decay of Dissipative Equations and Negative Sobolev Spaces
• Global existence and uniqueness result of a class of third-grade fluids equations
• Non-Uniform Decay of MHD Equations With and Without Magnetic Diffusion
• Decay rate for the incompressible flows in half spaces

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