Global solution to a one-dimensional model of viscous and heat-conducting micropolar real gas flow

Bašić-Šiško, Angela; Črnjarić-Žic, Nelida

doi:10.1016/j.jmaa.2020.124690

Cited by 11 publications

(22 citation statements)

References 27 publications

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“…We would like to point out that in Baši ć-Šiško and Draži ć, 23 it was proved that, assuming that Theorem 1 holds, the generalized solution exists globally in time, that is, in any time interval of finite length. Therefore, the proof of this theorem is essential for the formal completion of a global existence theorem.…”

Section: Statement Of the Problemmentioning

confidence: 97%

“…By taking into account expressions ( 12)-( 14), ( 27)- (28), from ( 21)- (23), we obtain the following Cauchy problem:…”

Section: Approximate Solutionsmentioning

confidence: 99%

“…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 Baši ć-Šiško and Draži ć22, 23 ).…”

Section: Introductionmentioning

confidence: 98%

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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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Section: Statement Of the Problemmentioning

confidence: 97%

“…By taking into account expressions ( 12)-( 14), ( 27)- (28), from ( 21)- (23), we obtain the following Cauchy problem:…”

Section: Approximate Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

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 shall prove the regularity and exponential stability of the solution in H 4 . The cylinder symmetric in the Eulerian coordinates in bounded annular domains G = {(x 1 , x 2 , x 3 ) ∈ R 3 , 0 < a < r < b < +∞, x 3 ∈ R, r = x 2 1 + x 2 2 } can be described by the following equations (see [26]): Here ρ, v, w, θ are the density, the velocity, microrotation velocity and absolute temperature. κ, R, c V , j I are the thermal conductivity, the gas constant, the specific heat capacity, microinertia density, respectively.…”

mentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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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Global existence theorem of a generalized solution for a one‐dimensional thermal explosion model of a compressible micropolar real gas

Bašić‐Šiško,

Dražić

2024

Math Methods in App Sciences

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We consider 1‐D thermal explosion of a compressible micropolar real gas, assuming that the initial density and temperature are bounded from below with a positive constant and that the initial data are sufficiently smooth. The starting problem is transformed into the Lagrangian description on the spatial domain and contains homogeneous boundary conditions. In this work, we prove that our problem has a generalized solution for any time interval . The proof is based on the local existence theorem and the extension principle.

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Global solution to a one-dimensional model of viscous and heat-conducting micropolar real gas flow

Cited by 11 publications

References 27 publications

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

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

Global existence theorem of a generalized solution for a one‐dimensional thermal explosion model of a compressible micropolar real gas

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