Existence Theorems for the 3D–Navier–Stokes System Having as Initial Conditions Sums of Plane Waves

2007 ◽  
pp. 289-300 ◽  
Author(s):  
Efim Dinaburg ◽  
Yakov Sinai
Keyword(s):  
Stokes System ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Plane Waves ◽  
Navier Stokes

ABSENCE OF THE LOCAL EXISTENCE THEOREM IN THE CRITICAL SPACE FOR THE $3\mathcal{D}$-NAVIER–STOKES SYSTEM

2005 ◽  
Vol 15 (11) ◽  
pp. 3635-3637
Author(s):  
YAKOV SINAI
Keyword(s):  
Nonlinear Integral Equation ◽  
Stokes System ◽  
Initial Conditions ◽  
Local Existence ◽  
Navier Stokes ◽  
External Forcing ◽  
Unique Global Solution ◽  
Local Existence Theorem ◽  
Local Solutions ◽  
Nonlocal Nonlinear

We consider the [Formula: see text]-Navier–Stokes System (NSS) on R3 without external forcing. After Fourier transform we get a nonlocal nonlinear integral equation equivalent to NSS. For one-parameter families of initial conditions A · c(0)(k)/|k|2 in the case of small |A| the NSS has a unique global solution. We argue that for large A NSS has no local solutions with these initial conditions.

scholarly journals Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

Sign in / Sign up

Export Citation Format

Share Document