# Questions tagged [navier-stokes]

The navier-stokes tag has no usage guidance.

25
questions

**0**

votes

**0**answers

46 views

### Inf sup condition for discrete Stokes problem

I am considering the discrete inf-sup condition for the discrete Stokes problem
$ \inf_{q \in Q_h} \sup_{v \in V_h} \frac{(q, \nabla \cdot v)}{\| q \| \| \nabla v\|} \geq \beta > 0$
This means ...

**1**

vote

**0**answers

35 views

### Density gradient of Navier-Stokes equations in perforated domain

Question: Is it possible to bound the density gradient $\nabla \rho_\epsilon$ of strong solutions to the compressible NSE uniformly in $L^\gamma$?
Preliminaries: Consider a bounded connected domain $\...

**1**

vote

**1**answer

129 views

### Leray projector in $L^{\infty}$ and negative order Besov spaces for the Navier-Stokes equations

I was reading the paper "Norm inflation for the generalized Navier-Stokes equations" which can be found here: https://arxiv.org/abs/1212.3801.
In Lemma 2.1, the authors said for any $\phi \in L^{\...

**0**

votes

**0**answers

16 views

### About parametrization of the interface of a fluid

In Navier Stokes Equation, more precisly in the evolution of a fluid interface I have an extension of the function $u$ such that:
$$u(x,t)=\frac{1}{2\pi} \operatorname{P.V.}\int_\Omega\frac{(x-z(\...

**2**

votes

**1**answer

93 views

### Cylindrical coordinates in axis symmetric flow

I am getting stuck in a detail in a paper. It's about the axi symmetric Navier Stokes equations
$$u_t - \nu\,\Delta u + u\cdot \nabla u + \nabla p=0$$
We consider in cylindrical coordinates $u=(u^r, u^...

**1**

vote

**0**answers

71 views

### 2D Stochastic Navier Stokes equations with Navier boundary condition

For the 2D Stochastic Navier Stokes equations with Navier boundary condition $$du = (\Delta u - u\cdot \nabla u - \nabla p)dt + \Phi dW$$ where we consider additive white noise here. I want to use the ...

**5**

votes

**1**answer

243 views

### Obstruction to Navier-Stokes blowup with cylindrical symmetry

Is there a known obstruction to cylindrically symmetric solutions (with swirl) of incompressible 3D Navier-Stokes blowing up in finite time ?
EDIT: in the whole space $\mathbb R^3$, I forgot to say.
...

**2**

votes

**0**answers

55 views

### Parabolic regularity for the 2D Navier-Stokes equations in a bounded domain

Suppose we consider 2D Navier-Stokes equations in a bounded domain $\Omega \subseteq \mathbb R^2$, together with suitable boundary conditions so that we can consider the vorticity equation: $$\omega_t ...

**3**

votes

**0**answers

75 views

### Green's function of time-dependent Stokes equation

It is well known that the Green's function of a standard parabolic equation in a bounded domain, say
\begin{align}
\partial_tG(x,y,t)-\Delta_x G(x,y,t)&=0
&&\mbox{for}\,\,\,(x,t)\in \...

**4**

votes

**1**answer

148 views

### Incompressible Navier-Stokes equation with heat conduction

How does the incompressible Navier-Stokes system read with heat conduction?
Where can I find an existence result for its weak solutions?

**3**

votes

**1**answer

122 views

### Difference between linear and parabolic velocity profiles in Stokes flows of two fluids

For droplet interactions in low-Reynolds number flow, solutions are available when the underlying flow can be written as linear compositions of strain and rotation, see Batchelor & Green (1972a).
...

**3**

votes

**1**answer

253 views

### Stationary Navier-Stokes solutions

Are there known nontrivial ($u\neq0$) stationary solutions to Navier-Stokes equations in $\mathbb R^3$ ? Not square integrable of course (that's impossible), but with self-similar amplitudes of ...

**4**

votes

**0**answers

133 views

### Estimate of $\Vert \nabla u \Vert_{L^{\infty}(\Omega)}$ of Navier Stokes equations

My question is how to estimate the term $\Vert \nabla u \Vert_{L^{\infty}(\Omega)}$. Here we consider the 2D incompressible Navier Stokes equations:$$u_t -\Delta u+u\cdot \nabla u+\nabla p=f$$ and $$\...

**11**

votes

**2**answers

961 views

### Has it been proved that weak solutions to the Navier-Stokes equations are non-unique, and does this prove that the Navier-Stokes are not valid?

This preprint claims that, for finite kinetic energy initial solutions, uniqueness of weak solutions to the Navier-Stokes equations doesn't hold:
https://arxiv.org/abs/1709.10033
What's the current ...

**3**

votes

**1**answer

104 views

### A solution to the Navier-Stokes equation that is defined for on $[0,T]$ with $T$ large is global?

Let $u_0 \in \dot{H}^{1/2}(\mathbb{R}^3)$. The Fujita-Kato theorem gives rise to a local unique solution $(t,x) \mapsto u(t,x)$ to the Navier-Stokes equations $$\left\{
\begin{array}{ccc}
\partial _t ...

**1**

vote

**1**answer

81 views

### Vorticity equation for generalized Naiver Stokes equations

In $3D$ or $2D$, I can get the vorticity equation for the incompressible NSE; however, what's the vorticity equation for the generalized NSE? Does the fractional laplacian commute with the curl?

**3**

votes

**0**answers

178 views

### Critical spaces and energy estimate in NS equation [closed]

There is a ‘rescaling transformation’ that is particularly significant for
the Navier–Stokes equations when they are posed on the whole space, but is
also important in the local regularity theory.
...

**2**

votes

**1**answer

204 views

### Hadamard-Rybczynski problem

HR problem deals with a spherical fluid viscous drop falling in a different fluid under influence of gravity. The outer fluid is of uniform speed $U$ in direction of gravity, far away from the drop. ...

**2**

votes

**1**answer

353 views

### Naviers Stokes equation and machine learning

I am looking for a reference explaining how to solve Navier-Stokes numerically using Machine learning algorithms .
Thank you in advance for your help .

**0**

votes

**1**answer

98 views

### Mild solution of 2D surface quasi-geostrophic (SQG) equation

I was reading one of Kato's papers on Navier-stokes equations. A mild solution can be denoted as $u= e^{t\Delta}u_0 + \int_{0}^{t} e^{(t-s)\Delta} \mathbb P\nabla \cdot(u \otimes u)ds$, where $\mathbb ...

**0**

votes

**1**answer

87 views

### Bound of solutions by initial value of Navier Stokes equations

For the mollified Navier Stokes equations: $$\partial_t u_{\epsilon} - \Delta u_{\epsilon} + \mathbb P \nabla \cdot((u_{\epsilon} \ast \omega_{\epsilon})\otimes u_{\epsilon})=0 $$ $$\nabla \cdot u_{\...

**2**

votes

**1**answer

139 views

### Fourier multiplier and Navier Stokes equations

Let $\mu$ be in $\mathcal D (\mathbb R^d)$ with $\mu \geq 0$, i.e. $\mu$ is a test function. Furthermore, we assume $\mu (\xi) =1$ when $|\xi|<1$ and $\mu (\xi) =0$ when $|\xi| \geq 2$. Why is the ...

**0**

votes

**1**answer

215 views

### A detail in Kato's paper (Strong $L^p$-Solutions of the Navier-Stokes Equation in $\mathbb R^m$, with Applications to Weak Solutions)

A detail in Kato's paper (Strong $L^p$-Solutions of the Navier-Stokes Equation
in $\mathbb R^m$, with Applications to Weak Solution).
Here is the link: http://junon.u-3mrs.fr/monniaux/K84.pdf
In the ...

**3**

votes

**0**answers

71 views

### Books on turbulent compressible fluid (gas) in heated channel

It's been a while I got my hands dirty with simulation of hydrodynamics and it was mostly incompressible and laminar. Now, I need to model turbulent flow in channel with additional external heating ...

**2**

votes

**0**answers

245 views

### Dual space of vector fields with null divergence

Let us consider $\mathscr D(\mathbb R^3;\mathbb R^3)$ the space of smooth compactly supported vector fields in $\mathbb R^3$ and let us define
$\widetilde{\mathscr D}=\mathscr D(\mathbb R^3;\mathbb R^...