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Results tagged with ap.analysis-of-pdes
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user 8901
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
0
votes
1
answer
641
views
Is this (interpolation) inequality right?
Suppose that $\Omega$ is a bounded domain in $\mathbb{R}^3$, $F$ is bounded in $L^\infty (\Omega \times (0,T))\cap (\cap_{k=1}^\infty L^{5/3}(0,T;C^k(\bar{\Omega})))$.
Question: Can we say that $F$ …
- 61
6
votes
2
answers
1k
views
How to solve the linearized Navier-Stokes equations in L^P?
Let $\Omega\subset \mathbb{R}^3$ be an open set with smooth boundary $\partial \Omega$.
Consider the following linearized Navier-Stokes equations in $Q_T=\Omega\times (0,T)$ for an arbitrarily fixed $ …
- 61