A. A. Zlotnik, A. A. Amosov, “Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases”, Mat. Zametki, 63:6 (1998), 835–846; Math. Notes, 63:6 (1998), 736

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Matematicheskie Zametki, 1998, Volume 63, Issue 6, Pages 835–846
DOI: https://doi.org/10.4213/mzm1353 (Mi mzm1353)

This article is cited in 24 scientific papers (total in 24 papers)

Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases

A. A. Zlotnik, A. A. Amosov

Moscow Power Engineering Institute (Technical University)

Full-text PDF (239 kB) Citations (24)

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DOI: https://doi.org/10.4213/mzm1353

Abstract: Nonhomogeneous initial boundary value problems for a specific quasilinear system of equations of composite type are studied. The system describes the one-dimensional motion of a viscous perfect polytropic gas. We assume that the initial data belong to the spaces

L_{\infty} (Ω)

$L_\infty(\Omega)$ or

L_{2} (Ω)

$L_2(\Omega)$ and the problems under consideration have generalized solutions only. For such solutions, a theorem on strong stability is proved, i.e., estimates for the norm of the difference of two solutions are expressed in terms of the sums of the norms of the differences of the corresponding data. Uniqueness of generalized solutions is a simple consequence of this theorem.

Received: 27.06.1996

English version:
Mathematical Notes, 1998, Volume 63, Issue 6, Pages 736–746
DOI: https://doi.org/10.1007/BF02312766

Bibliographic databases:

UDC: 517.958+533.7

Language: Russian

Citation: A. A. Zlotnik, A. A. Amosov, “Stability of generalized solutions to equations of one-dimensional motion of viscous heat-conducting gases”, Mat. Zametki, 63:6 (1998), 835–846; Math. Notes, 63:6 (1998), 736–746

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/mzm1353

https://www.mathnet.ru/eng/mzm/v63/i6/p835

This publication is cited in the following 24 articles:

Jinkai Li, Zhouping Xin, “Instantaneous Unboundedness of the Entropy and Uniform Positivity of the Temperature for the Compressible Navier–Stokes Equations with Fast Decay Density”, SIAM J. Math. Anal., 56:3 (2024), 3004
Gui-Qiang G. Chen, Yucong Huang, Shengguo Zhu, “Global Spherically Symmetric Solutions of the Multidimensional Full Compressible Navier–Stokes Equations with Large Data”, Arch Rational Mech Anal, 248:6 (2024)
Jinkai Li, Yasi Zheng, “Local Existence and Uniqueness of Heat Conductive Compressible Navier–Stokes Equations in the Presence of Vacuum Without Initial Compatibility Conditions”, J. Math. Fluid Mech., 25:1 (2023)
Jinkai Li, Zhouping Xin, “Local and global well-posedness of entropy-bounded solutions to the compressible Navier-Stokes equations in multi-dimensions”, Sci. China Math., 66:10 (2023), 2219
Tariq Mahmood, Zhaoyang Shang, Mei Sun, “On the vanishing elastic limit of compressible liquid crystal material flow”, Math Methods in App Sciences, 46:9 (2023), 10480
Mahmood T., Sun M., “Global Solution to the Compressible Non-Isothermal Nematic Liquid Crystal Equations With Constant Heat Conductivity and Vacuum”, Adv. Differ. Equ., 2021:1 (2021), 517
Li J., Xin Zh., “Entropy-Bounded Solutions to the One-Dimensional Heat Conductive Compressible Navier-Stokes Equations With Far Field Vacuum”, Commun. Pure Appl. Math., 2021
Li J., Xin Zh., “Entropy Bounded Solutions to the One-Dimensional Compressible Navier-Stokes Equations With Zero Heat Conduction and Far Field Vacuum”, Adv. Math., 361 (2020), 106923
Li J., “Global Well-Posedness of Non-Heat Conductive Compressible Navier-Stokes Equations in 1D”, Nonlinearity, 33:5 (2020), 2181–2210
Li J., “Global Small Solutions of Heat Conductive Compressible Navier-Stokes Equations With Vacuum: Smallness on Scaling Invariant Quantity”, Arch. Ration. Mech. Anal., 237:2 (2020), 899–919
Gong H., Li J., Liu X.-G., Zhang X., “Local Well-Posedness of Isentropic Compressible Navier-Stokes Equations With Vacuum”, Commun. Math. Sci., 18:7 (2020), 1891–1909
Dou Ch., Xu Ya., 4Th International Conference on Advances in Energy Resources and Environment Engineering, IOP Conf. Ser. Earth Envir. Sci., IOP Conference Series-Earth and Environmental Science, 237, IOP Publishing Ltd, 2019
Li Ya. Jiang L., “Global Weak Solutions For the Cauchy Problem to One-Dimensional Heat-Conductive Mhd Equations of Viscous Non-Resistive Gas”, Acta Appl. Math., 163:1 (2019), 185–206
Li J., “Global Well-Posedness of the One-Dimensional Compressible Navier-Stokes Equations With Constant Heat Conductivity and Nonnegative Density”, SIAM J. Math. Anal., 51:5 (2019), 3666–3693
Alexander Zlotnik, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2018, 2421
Fan J., Huang Sh., Li F., “Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum”, Kinet. Relat. Mod., 10:4 (2017), 1035–1053
Alexander Zlotnik, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 2016, 1
Fan J. Jiang S. Nakamura G., “Stability of Weak Solutions to Equations of Magnetohydrodynamics with Lebesgue Initial Data”, J. Differ. Equ., 251:8 (2011), 2025–2036
Fan, JS, “Stability of weak solutions to the compressible Navier–Stokes equations in bounded annular domains”, Mathematical Methods in the Applied Sciences, 31:2 (2008), 179
Jiang, S, “Global well-posedness of the Cauchy problem for the equations of a one-dimensional viscous heat-conducting gas with Lebesgue initial data”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 134 (2004), 939

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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