Weak Solutions for Compressible Navier–Stokes–Fourier System in Two Space Dimensions with Adiabatic Exponent Almost One

Abstract

We study the evolutionary compressible Navier–Stokes–Fourier system in a bounded two-dimensional domain with the pressure law $p(\varrho ,\theta ) \sim \varrho \theta + \varrho \log ^{\alpha }(1+ \varrho )+ \theta ^{4}$ . We consider the weak solutions with entropy inequality and total energy balance. We show the existence of this type of weak solutions without any restriction on the size of the initial conditions or the right-hand sides provided $\alpha > \frac{17+\sqrt{417}}{16}\cong 2.34$ .