Uniqueness of generalized solution to micropolar viscous real gas flow with homogeneous boundary conditions

Bašić-Šiško, Angela; Črnjarić-Žic, Nelida

doi:10.1002/mma.7032

Cited by 11 publications

(10 citation statements)

References 28 publications

(66 reference statements)

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“…This type of fluid has been considered in the classical case in the context of several mathematical problems, considering in particular the problem of the existence of a solution, the problem of regularity, and the problem of stabilization of the solution [29][30][31][32][33][34]. For the micropolar case of a real fluid in one dimension, the local and global existence and the uniqueness of the generalized solution have been proved so far [35][36][37].…”

Section: Literature Review and Important Resultsmentioning

confidence: 99%

Uniqueness of a Generalized Solution for a One-Dimensional Thermal Explosion Model of a Compressible Micropolar Real Gas

Bašić-Šiško,

Dražić

2024

Mathematics

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In this paper, we analyze a quasi-linear parabolic initial-boundary problem describing the thermal explosion of a compressible micropolar real gas in one spatial dimension. The model contains five variables, mass density, velocity, microrotation, temperature, and the mass fraction of unburned fuel, while the associated problem contains homogeneous boundary conditions. The aim of this work is to prove the uniqueness theorem of the generalized solution for the mentioned initial-boundary problem. The uniqueness of the solution, together with the proven existence of the solution, makes the described initial-boundary problem theoretically consistent, which provides a basis for the development of numerical methods and the engineering application of the model.

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Section: Literature Review and Important Resultsmentioning

confidence: 99%

Uniqueness of a Generalized Solution for a One-Dimensional Thermal Explosion Model of a Compressible Micropolar Real Gas

Bašić-Šiško,

Dražić

2024

Mathematics

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“…Therefore, the proof of this theorem is essential for the formal completion of a global existence theorem. It is also already proved that this model has at most one solution 22 …”

Section: Statement Of the Problemmentioning

confidence: 91%

“…The proof is divided into a sequence of lemmas and is based on the a priori estimates of the approximate solutions. The authors of this paper have already published some important results on this model (see Bašić‐Šiško and Dražić 22,23 ).…”

Section: Introductionmentioning

confidence: 94%

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Local existence theorem for micropolar viscous real gas flow with homogeneous boundary conditions

Bašić-Šiško

Črnjarić-Žic

2022

Math Methods in App Sciences

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We consider the model for one-dimensional micropolar, viscous, polytropic, and thermally conductive real gas flow with homogeneous boundary conditions, using the generalized equation of state for pressure. The generalization is shown by the fact that the pressure depends on the mass density as a power function. The governing system of partial differential equations is given in the Lagrangian description. Using the Faedo-Galerkin method and a priori estimates, we prove that the generalized solution exists locally in time.

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“…Later on, she established the global existence for non-homogeneous boundary conditions in [33]. Recently, for the onedimensional model of viscous and heat-conducting micropolar real gas flow, Dražić et al [16,2,3] proved the numerical solution, global existence theorem, and the uniqueness of generalized solution.…”

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Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry

Huang¹,

Sun²,

Yang³

et al. 2022

CPAA

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<p style='text-indent:20px;'>This paper is concerned with the global solutions of the 3D compressible micropolar fluid model in the domain to a subset of <inline-formula><tex-math id="M1">\begin{document}$ R^3 $\end{document}</tex-math></inline-formula> bounded with two coaxial cylinders that present the solid thermo-insulated walls, which is in a thermodynamical sense perfect and polytropic. Compared with the classical Navier-Stokes equations, the angular velocity <inline-formula><tex-math id="M2">\begin{document}$ w $\end{document}</tex-math></inline-formula> in this model brings benefit that is the damping term -<inline-formula><tex-math id="M3">\begin{document}$ uw $\end{document}</tex-math></inline-formula> can provide extra regularity of <inline-formula><tex-math id="M4">\begin{document}$ w $\end{document}</tex-math></inline-formula>. At the same time, the term <inline-formula><tex-math id="M5">\begin{document}$ uw^2 $\end{document}</tex-math></inline-formula> is bad, it increases the nonlinearity of our system. Moreover, the regularity and exponential stability in <inline-formula><tex-math id="M6">\begin{document}$ H^4 $\end{document}</tex-math></inline-formula> also are proved.</p>

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Uniqueness of generalized solution to micropolar viscous real gas flow with homogeneous boundary conditions

Cited by 11 publications

References 28 publications

Uniqueness of a Generalized Solution for a One-Dimensional Thermal Explosion Model of a Compressible Micropolar Real Gas

Uniqueness of a Generalized Solution for a One-Dimensional Thermal Explosion Model of a Compressible Micropolar Real Gas

Local existence theorem for micropolar viscous real gas flow with homogeneous boundary conditions

Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry

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