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Inviscid limit for the damped generalized incompressible Navier-Stokes equations on $ \mathbb{T}^2 $

  • * Corresponding author: Chunyou Sun

    * Corresponding author: Chunyou Sun
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  • In this paper, for the damped generalized incompressible Navier-Stokes equations on $ \mathbb{T}^{2} $ as the index $ \alpha $ of the general dissipative operator $ (-\Delta)^{\alpha} $ belongs to $ (0,\frac{1}{2}] $, we prove the absence of anomalous dissipation of the long time averages of entropy. We also give a note to show that, by using the $ L^{\infty} $ bounds given in Caffarelli et al. [4], the absence of anomalous dissipation of the long time averages of energy for the forced SQG equations established in Constantin et al. [12] still holds under a slightly weaker conditions $ \theta_{0}\in L^{1}(\mathbb{R}^{2})\cap L^{2}(\mathbb{R}^{2}) $ and $ f \in L^{1}(\mathbb{R}^{2})\cap L^{p}(\mathbb{R}^{2}) $ with some $ p > 2 $.

    Mathematics Subject Classification: Primary: 35K05, 35Q30, 76D05.


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