Mild solutions to the time fractional Navier-Stokes equations in R-N

@article{CarvalhoNeto2015MildST,
  title={Mild solutions to the time fractional Navier-Stokes equations in R-N},
  author={Paulo Mendes de Carvalho-Neto and Gabriela Planas},
  journal={Journal of Differential Equations},
  year={2015},
  volume={259},
  pages={2948-2980}
}

On the time-fractional Navier-Stokes equations

Approximate controllability for mild solution of time-fractional Navier–Stokes equations with delay

This paper addresses some results about mild solution to time-fractional Navier–Stokes equations with bounded delay existed in the convective term and the external force. Based on the Schauder’s

Mild solutions to the Cauchy problem for time-space fractional Keller-Segel-Navier-Stokes system

This paper investigates the Cauchy problem of the time-space fractional Keller-Segel-NavierStokes model in R (d ≥ 2) which can describe both memory effect and Lévy process of the system. The local

Mild solutions to the time fractional Navier-Stokes delay differential inclusions

In this paper, we study a Navier-Stokes delay differential inclusion with time fractional derivative of order \begin{document} $\alpha\in(0,1)$ \end{document} . We first prove the local and global

On the fractional chemotaxis Navier-Stokes system in the critical spaces

We consider the fractional chemotaxis Navier-Stokes equations which are the fractional Keller-Segel model coupled with the Navier-Stokes fluid in the whole space, and prove the existence of global

Local and Global Existence and Uniqueness of Solution for Time-Fractional Fuzzy Navier–Stokes Equations

Navier–Stokes (NS) equation, in fluid mechanics, is a partial differential equation that describes the flow of incompressible fluids. We study the fractional derivative by using fractional

Dissipativity of Fractional Navier–Stokes Equations with Variable Delay

We use classical Galerkin approximations, the generalized Aubin–Lions Lemma as well as the Bellman–Gronwall Lemma to study the asymptotical behavior of a two-dimensional fractional Navier–Stokes

Existence and approximations of solutions for time‐fractional Navier‐stokes equations

The purpose of this work is to investigate the problem of solutions to the time‐fractional Navier‐Stokes equations with Caputo derivative operators. We obtain the existence and uniqueness of the
...

References

SHOWING 1-10 OF 39 REFERENCES

Large-time behavior in incompressible Navier-Stokes equations

We give a development up to the second order for strong solutions u of incompressible Navier–Stokes equations in $\mathbb{R}^n $, $n \geq 2$. By combining estimates obtained from the integral

A generalization of a theorem by Kato on Navier-Stokes equations

We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,8);L3(R3)). More precisely, we show that if the initial data are sufficiently

Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods

In the present work, by introducing the fractional derivative in the sense of Caputo, the He's homotopy perturbation method (HPM) and variational iteration method (VIM) are used to study the

Fractional differential equations: a novel study of local and global solutions in Banach spaces

Motivated by the huge success of the applications of the abstract fractional equations in many areas of science and engineering, and by the unsolved question in this theory, in this work we study

Decay Results for Weak Solutions of the Navier–Stokes Equations on Rn

On considere les solutions faibles du probleme de Cauchy pour l'equation de Navier-Stokes sur R n , n≥2. On etablit des resultats concernant la decroissance de la L 2 -norme d'une solution faible

On Shinbrot’s conjecture for the Navier-Stokes equations

  • Kewei Zhang
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1993
Marvin Shinbrot conjectured that the weak solution of the Navier-Stokes equations possess fractional derivatives in time of any order less than 1/2. In this paper, using the Hardy-Littlewood maximal