Questions tagged [navier-stokes]
The navier-stokes tag has no usage guidance.
-2
votes
0answers
55 views
Implementing Numerically the Steady Navier Stokes Equation [closed]
I am trying to solve the Steady Navier Stokes equation in a two-dimensional domain.
I found a code online in freefem++ which at some point reads:
...
5
votes
1answer
159 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.
...
1
vote
0answers
31 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: $$\omega_t ...
3
votes
0answers
48 views
Green's function of time-dependent Stokes equation
It is well known that the Green's function of a standard parabolic equation in a bounded domain, say
\begin{align}
\partial_tG(x,y,t)-\Delta_x G(x,y,t)&=0
&&\mbox{for}\,\,\,(x,t)\in \...
4
votes
1answer
74 views
Incompressible Navier-Stokes equation with heat conduction
How does the incompressible Navier-Stokes system read with heat conduction?
Where can I find an existence result for its weak solutions?
6
votes
1answer
180 views
Navier-Stokes fluid dynamics, Einstein gravity and holography
There was some activity a while ago, like 10 years ago, string theoreists try to relate
the fluid dynamics, for example, governed by Navier-Stokes equation,
to
the Einstein gravity, and its ...
3
votes
1answer
48 views
Difference between linear and parabolic velocity profiles in Stokes flows of two fluids
For droplet interactions in low-Reynolds number flow, solutions are available when the underlying flow can be written as linear compositions of strain and rotation, see Batchelor & Green (1972a).
...
3
votes
1answer
180 views
Stationary Navier-Stokes solutions
Are there known nontrivial ($u\neq0$) stationary solutions to Navier-Stokes equations in $\mathbb R^3$ ? Not square integrable of course (that's impossible), but with self-similar amplitudes of ...
3
votes
0answers
114 views
Estimate of $\Vert \nabla u \Vert_{L^{\infty}(\Omega)}$ of Navier Stokes equations
My question is how to estimate the term $\Vert \nabla u \Vert_{L^{\infty}(\Omega)}$. Here we consider the 2D incompressible Navier Stokes equations:$$u_t -\Delta u+u\cdot \nabla u+\nabla p=f$$ and $$\...
11
votes
2answers
441 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 ...
1
vote
1answer
81 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
1answer
73 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?
0
votes
0answers
63 views
Estimate of $\|\nabla u\|_{L^{\infty}(\mathbb R^2)}$ for incompressible Navier-Stokes equations
Consider the incompressible Navier-Stokes equations on $\mathbb R^2:~u_t - \Delta u + u\cdot\nabla u + \nabla p=f$. I want to estimate $\|\nabla u\|_{L^{\infty}(\mathbb R^2)}$. Is there a way to ...
0
votes
0answers
15 views
Outflow boundary condition for characteristic-based split method (FEM)
Could anyone please explain me, how to implement outflow boundary conditions when solving Navier-Stokes equation for incompressible fluid using characteristic-based split method?
I'm trying to ...
1
vote
0answers
135 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
1answer
119 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
1answer
257 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
1answer
88 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
0answers
72 views
Bound of the bilinear form in Navier-Stokes equations
We consider the integral equation for the solution in (incompressible) Navier-Stokes equations: $u = e^{t\Delta}u_0 - \int_{0}^{t}e^{{(t-s)}\Delta} \mathbb P\nabla\cdot(u \otimes u)ds$. Then, consider ...
0
votes
1answer
80 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
1answer
125 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
1answer
192 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
0answers
66 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
0answers
191 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^...
