# 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} }

## 117 Citations

### Weak solutions of the time-fractional Navier-Stokes equations and optimal control

- MathematicsComput. Math. Appl.
- 2017

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

- MathematicsZeitschrift für angewandte Mathematik und Physik
- 2021

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

- Mathematics
- 2022

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

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2019

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

- MathematicsDiscrete and Continuous Dynamical Systems - B
- 2022

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

- MathematicsFractal and Fractional
- 2022

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

- MathematicsMathematics
- 2020

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

- Mathematics
- 2018

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

- Mathematics
- 1996

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

- Mathematics
- 1997

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

- Mathematics
- 2009

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

- Mathematics
- 2013

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…

### Cauchy problems for fractional differential equations with Riemann-Liouville fractional derivatives ✩

- Mathematics
- 2012

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

- Mathematics
- 1987

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…

### Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method

- MathematicsAppl. Math. Comput.
- 2006

### On Shinbrot’s conjecture for the Navier-Stokes equations

- MathematicsProceedings 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…