Well-Posedness and Asymptotic Behavior for Compressible Flows in One Dimension

Yuming Qin ()
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Yuming Qin: Donghua University, Department of Applied Mathematics, College of Science

Chapter 42 in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, pp 2325-2420 from Springer

Abstract: Abstract This short survey introduces some results on the global well-posedness and asymptotic behavior of strong (generalized) solutions (including the existence of universal (global) attractors) to the 1D nonstationary equations of viscous polytropic gases, heat-conducting gases, and barotropic gases. In Sect. 3, the existence theory framework of H i (i = 1, 2, 4)−global (generalized) solutions and global attractors of viscous real gases for the initial boundary value problem are introduced. In Sect. 4, such an existence theory framework for the Cauchy problem with some modifications is also given.

Date: 2018
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DOI: 10.1007/978-3-319-13344-7_34

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