Low-regularity solutions for the 2D fractional Voigt–Boussinesq system

We consider the 2D fractional Voigt regularization of the Boussinesq system. For fixed Voigt parameter, we construct global low-regularity weak solutions in a range of fractional exponents not covered by existing smooth-regularity results. We also prove an O(ε) convergence rate to the Boussinesq solution as the Voigt parameter tends to zero.