On the compressible micropolar fluids in a time-dependent domain

Huang, Bingkang; Nečasová, Šárka; Zhang, Lan

doi:10.1007/s10231-022-01218-6

Cited by 2 publications

(1 citation statement)

References 25 publications

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“…Classical compressible fluid is still a field with many open problems. In particular, the mathematical analysis of three-dimensional models [20], of models admitting an initial vacuum [21], and of models with time-dependent domains [22] stand out.…”

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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Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains

Bhandari,

Huang,

Nečasová

2024

Math. Models Methods Appl. Sci.

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In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill the full-slip boundary condition and the temperature on the boundary is given by a non-homogeneous Dirichlet condition. We establish the global-in-time weak solution to the system. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of ballistic energy is utilized in this work.

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On the compressible micropolar fluids in a time-dependent domain

Cited by 2 publications

References 25 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

Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains

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