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Some remarks to the compactness of steady compressible isentropic Navier-Stokes equations via the decomposition method. (English) Zbl 0852.76077
We investigate the title problem using the method of decomposition. We find the compactness of the incompressible part $$u$$ of the velocity field $$v$$ and we give a new proof of the compactness of the “effective pressure” $${\mathcal P} = \rho^\gamma - (2 \mu_1 + \mu_2) \text{div} v$$. We derive some new estimates of these quantities in Hardy and Triebel-Lizorkin spaces.

##### MSC:
 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q30 Navier-Stokes equations
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