The energy measure for the Euler equations: the endpoint case. (English) Zbl 07443293

Tan, Wenke

Appl. Math. Lett. 124, Article ID 107646, 7 p. (2022).

Summary: In this paper, we consider the energy measure \(\mathcal{E}\) for the Euler equations in the endpoint case \(u \in L^{2 , \infty} ( B M O ( \Omega ) )\) for any \(\Omega \subseteq \mathbb{R}^3\). We establish the lower bounds of the lower local dimension and concentration dimension of the energy measure \(\mathcal{E}\) at the first blow-up time.

MSC:

35Q31	Euler equations
81-XX	Quantum theory

Keywords:

Euler equations; energy measure; lower local dimension; concentration dimension

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