Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with ap.analysis-of-pdes
Search options not deleted
user 75422
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
Finding Free surface elevation in semi-infinite channel
What I seem to understand is that the bottom is at $y=-h+v(x-ct)$ where $v$ has compact support. That corresponds to an obstacle moving at a constant speed towards the infinite end. But it might mean …
- 3,085
2
votes
Stationary Navier-Stokes solutions
Tai-Peng Tsai's book Lectures on Navier-Stokes Equations (2018) cites as Theorem 8.3 (p.149) a theorem of V. Sverak (2011) that excludes the existence of minus one homogeneous solutions on $\mathbb R^ …
- 3,085
5
votes
1
answer
314
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.
…
- 3,085
6
votes
1
answer
423
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 Fourie …
- 3,085
0
votes
Dirichlet problem for capillary equation over convex domain
Prescribed mean curvature (of the graph of $u$) would be$$\nabla\cdot\frac{\nabla u}{\sqrt{1+|\nabla u|^2}}=c$$For an elliptic domain with $\phi$ linear in the direction of the smaller axis, the graph …
- 3,085
1
vote
On solutions of the continuity equation
If $j$ has compact support in $\mathbb R_t\times\mathbb R^3_x$, $\rho$ will have compact support iff $\int_{-\infty}^\infty\nabla\cdot j_s\ ds\equiv0$.
The set of approximable $L^2$ solutions should …
- 3,085
2
votes
Vorticity equation for generalized Naiver Stokes equations
Taking the curl of the original equation in $\mathbb R^3$ gives$$\partial_t\omega+\nu(-\Delta)^\alpha\omega+(u\cdot\nabla)\omega-(\omega\cdot\nabla) u=\nabla\times f$$ $$\nabla\times u=\omega$$ $$\nab …
- 3,085
1
vote
Accepted
Morrey condition (integral condition) and (local) Holder condition
No. Take $n=2$, $x=0$ (and $\alpha=1$, wlog). Define $f$ in polar coordinates as $f(r,\theta)=r^\beta g_r(\theta)$ where $\int_0^{2\pi} g_r(\theta)\ d\theta=1$ and $\lim_{r\to 0}g_r(0)=\infty$, which …
- 3,085
2
votes
Are Pointwise conditions studied?, do they make sense?, do they have any applications?
Such interpolatory conditions are better treated by solving your PDE $Af=\sum_ic_i\delta_{p_i}$ as distributions in the whole domain, with the $c_i$s to be determined so that $f(p_i)=d_i$. For ellipti …
- 3,085
5
votes
Gaussian distribution, maximum entropy and the heat equation
Besides the central limit theorem, there is the connection between diffusion and Wasserstein distance $W_2(p,q)$ (the minimum integral of squared distance from $x$ to $T(x)$ when $T$ maps $p$ to $q$) …
- 3,085
8
votes
1
answer
328
views
Continuous right inverse to the Laplacian operator on $C^\infty$
For each $f\in C^\infty(\mathbb R^n)$, there exists $u\in C^\infty(\mathbb R^n)$ such that $\Delta u=f$. This, I guess, has been known well before the more general Malgrange-Ehrenpreis theorem that sa …
- 3,085
2
votes
An acting condition for a superposition operator from $H^1(\Omega)$ to $H^1(\Omega)$
The obvious sufficient condition for $v\mapsto f(v)$ to map $H^1(\Omega)$ to itself ($\Omega$ bounded) is $f$ globally Lipschitz, i.e. $f'\in L^\infty(\mathbb R)$. Add $f(0)=0$ for general $\Omega$.
…
- 3,085
2
votes
Reformulation of the classical Navier-Stokes equation as a semilinear evolution equation and...
You are right, $(4)$ has to be understood in the special sense that the semigroup $S(t)$ (and the (Leray?) $L^2$-projection operator to $H$, as well) extend to a wider space, that of "distributional d …
- 3,085
2
votes
A $W^{1,2}_{loc}$ function with uniformly bounded integrals on compact subsets $W^{1,2}$?
Yes. There is an increasing sequence of compacts $K_n\subset\Omega$ whose union is $\Omega$, then $\int_{\Omega}(|f|^2+|\nabla f|^2)=\lim_{n\to\infty}\int_{K_n}(|f|^2+|\nabla f|^2)\le C$.
- 3,085
2
votes
1
answer
110
views
Smoluchowski-Poisson dynamics with atomic measures
"Smoluchowski-Poisson dynamics" is just a tentative provisional name I give to the following transport equation:$$\partial_t m+\nabla_x\cdot(um)=0$$where $u(x,t)\in\mathbb R^n$ ($x\in\mathbb R^n$, $t\ …
- 3,085