The global existence of strong solutions for a non-isothermal ideal gas system

We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space H² (ℝ³) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space \(\dot{\boldsymbol{B}}_{\boldsymbol{2,1}}^{\boldsymbol{3/2}}\) $${\dot{\mathit{B}}}_{\mathbf{2}\mathbf{,}\mathbf{1}}^{\mathbf{3}/\mathbf{2}}$$ by showing that the linearized operator is a contraction mapping under the right circumstances.