Calderón–Zygmund theory in Lorentz mixed‐norm spaces and its application to compressible fluids

Abstract

AbstractIn this paper, it is shown that the general Calderón–Zygmund singular integral operators including Riesz transforms are bounded on anisotropic Lorentz spaces with and . As an application, we establish some new blowup criteria involving temperature in its scaling‐invariant anisotropic Lorentz space for the 3D full compressible Navier–Stokes equations allowing vacuum and without additional conditions on viscosity coefficients except physical restrictions, which improve the previous corresponding results.