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Well-posedness and exponential decay for the Navier–Stokes equations of viscous compressible heat-conductive fluids with vacuum
Mathematical Models and Methods in Applied Sciences ( IF 3.5 ) Pub Date : 2022-09-27 , DOI: 10.1142/s0218202522500403
Suhua Lai , Hao Xu , Jianwen Zhang

This paper is concerned with the Cauchy problem of Navier–Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in 3. For less regular data and weaker compatibility condition than those proposed by Cho–Kim [Existence results for viscous polytropic fluids with vacuum, J. Differ. Equ. 228 (2006) 377–411], we first prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is more regular. We also establish the global well-posedness of classical solutions with large oscillations and vacuum in the case when the initial total energy is suitably small. The exponential decay estimates of the global solutions are obtained.



中文翻译:

具有真空的粘性可压缩导热流体的 Navier-Stokes 方程的适定性和指数衰减

本文关注在无穷远处具有远场真空的可压缩粘性导热流体的 Navier-Stokes 方程的 Cauchy 问题3. 对于比 Cho-Kim 提出的那些更不规则的数据和更弱的相容性条件 [Existence results for viscous polytropic fluids with Vacuum, J. Differ。等。 228 (2006) 377-411],我们首先证明了属于更大类函数的局部实时解的存在,其中唯一性可以被证明是成立的。如果初始密度更规则,则局部解实际上是远离初始时间的经典解。在初始总能量适当小的情况下,我们还建立了具有大振荡和真空的经典解的全局适定性。获得了全局解的指数衰减估计。

更新日期:2022-09-27
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