This work demonstrates global well-posedness and optimal decay rates for solutions in compressible fluids, indicating significant contributions to fluid dynamics understanding.
In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases. First of all, we study the global well-posedness of the Cauchy problem to the system when the initial data is small enough. Secondly, we show the optimal decay rates of the higher-order spatial derivatives of the Ḣ⁻ˢ (0≤ s<3/2) negative Sobolev norms. Finally, under the assumption that the initial data is bounded in L¹-norm, we establish the upper and lower bounds of the optimal decay rates for the classical solutions.
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Huo et al. (2025) studied this question.
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