Time-space $L^2$-boundedness for the 2D Navier-Stokes equations and hyperbolic Navier-Stokes equations

2019 ◽  
Vol 43 (2) ◽  
pp. 223-239
Author(s):  
Takayuki Kobayashi ◽  
Masashi Misawa ◽  
Kenji Nakamura
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Space

Well-posedness of the time-space fractional stochastic Navier-Stokes equations driven by fractional Brownian motion

2018 ◽  
Vol 13 (1) ◽  
pp. 11 ◽  
Author(s):  
Pengfei Xu ◽  
Caibin Zeng ◽  
Jianhua Huang
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Banach Fixed Point Theorem ◽  
Well Posedness ◽  
Stochastic Convolution ◽  
Navier Stokes Equations ◽  
Time Space

The current paper is devoted to the time-space fractional Navier-Stokes equations driven by fractional Brownian motion. The spatial-temporal regularity of the nonlocal stochastic convolution is firstly established, and then the existence and uniqueness of mild solution are obtained by Banach Fixed Point theorem and Mittag-Leffler families operators.

scholarly journals Generation and solutions to the time-space fractional coupled Navier-Stokes equations

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3899-3905
Author(s):  
Chang-Na Lu ◽  
Sheng-Xiang Chang ◽  
Luo-Yan Xie ◽  
Zong-Guo Zhang
Keyword(s):  
Exact Solutions ◽  
Inverse Method ◽  
Fractional Derivatives ◽  
Variational Principles ◽  
Stokes Equations ◽  
Lagrange Equation ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Space

In this paper, a Lagrangian of the coupled Navier-Stokes equations is proposed based on the semi-inverse method. The fractional derivatives in the sense of Riemann-Liouville definition are used to replace the classical derivatives in the Lagrangian. Then the fractional Euler-Lagrange equation can be derived with the help of the fractional variational principles. The Agrawal?s method is devot?ed to lead to the time-space fractional coupled Navier-Stokes equations from the above Euler-Lagrange equation. The solution of the time-space fractional coupled Navier-Stokes equations is obtained by means of RPS algorithm. The numerical results are presented by using exact solutions.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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