The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study o...The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.展开更多
We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a nei...We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of a trivially stationary solution.The appearance of the difference between energy gained and energy lost due to the reaction is a new feature for the flow and brings new difficulties.To handle these,we construct a new linearized system in terms of a combination of the solutions.Moreover,some optimal timedecay estimates of the solutions are derived when the initial perturbation is additionally bounded in L1.It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solution so that the long time behavior for the hyperbolic-parabolic system is exactly the same as that for the heat equation.As a byproduct,the above time-decay estimate at the highest order is also valid for compressible Navier-Stokes equations.The proof is accomplished by virtue of Fourier theory and a new observation for cancellation of a low-medium-frequency quantity.展开更多
基金supported by the National Natural Science Foundation of China(11722104,11671150)supported by the National Natural Science Foundation of China(11571280,11331005)+3 种基金supported by the National Natural Science Foundation of China(11331005,11771150)by GDUPS(2016)the Fundamental Research Funds for the Central Universities of China(D2172260)FANEDD No.201315
文摘The two-phase flow models are commonly used in industrial applications, such as nuclear, power, chemical-process, oil-and-gas, cryogenics, bio-medical, micro-technology and so on. This is a survey paper on the study of compressible nonconservative two-fluid model, drift-flux model and viscous liquid-gas two-phase flow model. We give the research developments of these three two-phase flow models, respectively. In the last part, we give some open problems about the above models.
基金supported by National Natural Science Foundation of China(Grant Nos.11871341 and 11571231)supported by National Natural Science Foundation of China(Grant Nos.11671150 and 11722104)。
文摘We consider the full compressible Navier-Stokes equations with reaction diffusion.A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of a trivially stationary solution.The appearance of the difference between energy gained and energy lost due to the reaction is a new feature for the flow and brings new difficulties.To handle these,we construct a new linearized system in terms of a combination of the solutions.Moreover,some optimal timedecay estimates of the solutions are derived when the initial perturbation is additionally bounded in L1.It is worth noticing that there is no decay loss for the highest-order spatial derivatives of the solution so that the long time behavior for the hyperbolic-parabolic system is exactly the same as that for the heat equation.As a byproduct,the above time-decay estimate at the highest order is also valid for compressible Navier-Stokes equations.The proof is accomplished by virtue of Fourier theory and a new observation for cancellation of a low-medium-frequency quantity.
