All Questions
7 questions with no upvoted or accepted answers
3
votes
0
answers
182
views
Parabolic regularization for the Navier-Stokes equations
I'm looking for some references about a result on the Navier-Stokes equations which seems to be folklore but for which I didn't manage to find a proof. The setting is the following :
Let $Q=\mathbb{R}^...
- 161
3
votes
0
answers
104
views
Regular Lagrangian flows on a domain of $\mathbb{R}^d$ with a boundary
I'm looking for some references about the theory of regular Lagrangian flows on a smooth domain $\Omega$ of $\mathbb{R}^d$ (say a smooth bounded open set of $\mathbb{R}^d$ or a half space).
Here, ...
- 161
2
votes
0
answers
126
views
Differential equations: trying to connect a nonlinear equation to a linear one
The following is motivated by taking a product space $\Omega$ and splitting it into two parts via projections, whose subspaces, $T$ and $X$, are home to functions which satisfy a nonlinear PDE and a ...
- 383
2
votes
0
answers
79
views
Point Spectrum of a Second Order System of Differential Equations
Consider the following operator acting on $H^1(\mathbb{R})$
$$
\mathcal{L} \left(\begin{array}{c} \phi \\ \psi \end{array}\right) = -\left(\begin{array}{c} \phi \\ \psi \end{array}\right)'' + V(x) \...
- 516
1
vote
0
answers
147
views
Property of Fixed Point Function
Given an operator $\mathcal{T}$ that maps from a function $f: \mathbb{R}^d\rightarrow \mathbb{R}$ to another function $f': \mathbb{R}^d\rightarrow \mathbb{R}$, we are interested in the fixed point $f^*...
- 1,127
1
vote
0
answers
154
views
Lyapunov stability for nonlinear PDEs
Where can I find a theorem about Lyapunov stability for the equation in Hilbert space?
$$
y' = Fy,
$$
where $F : V \to V'$ is a nonlinear operator , $y' \in L^2(0,T,V')$, $V$ is a Hilbert space.
...
- 243
0
votes
0
answers
72
views
Di Perna-Lions theory for transport equations with an additional integral operator
I'm looking for a reference about some possible generalization of the well-known Di Perna-Lions theory for transport equations (say, on $[0,T] \times \mathbb{R}^d$) of the form
\begin{align}
\...
- 161