Abstract
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 \(\dot{\boldsymbol{B}}_{\boldsymbol{2,1}}^{\boldsymbol{3/2}}\) by showing that the linearized operator is a contraction mapping under the right circumstances.
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The authors would like to express their sincere gratitude to professor Chun Liu for helpful discussions.
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The first author was partially supported by the Zhejiang Province Science Fund (LY21A010009). The second author was partially supported by the National Science Foundation of China (12271487, 12171097). The third author was partially supported by the National Science Foundation (DMS-2012333, DMS-2108209).
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Han, B., Lai, N. & Tarfulea, A. The global existence of strong solutions for a non-isothermal ideal gas system. Acta Math Sci 44, 865–886 (2024). https://doi.org/10.1007/s10473-024-0306-9
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DOI: https://doi.org/10.1007/s10473-024-0306-9