The Study Of The Cauchy Problem For Two Compressible Two-Phase Flow Equations

Fluid dynamics is an important branch of fluid mechanics,which mainly studies the motion state and law of fluid in continuum under the action of force.Mathematically,its main characterization tool is the fluid dynamics equation.This paper is devoted to studying the Cauchy problem for the multidimensional compressible non-conservative two-fluid equations and the multidimensional compressible liquid-gas two-phase flow equations.In Chapter 1,we mainly introduce the research background and significance of multidimensional compressible non-conservative two-fluid equations and multidimensional compressible liquid-gas two-phase flow equations,the research status at home and abroad and the main content of this paper.In Chapter 2,we present the functional spaces,several useful inequalities,the localization theory of frenqency functional spaces and some important lemmas.In Chapter 3,we obtain the existence of global strong solutions to the multidimensional non-conservative compressible two-fluid model with capillarity effects in any dimension≥2under the assumptions on some large initial data.Our analysis mainly relies on Fourier frequency localization technology,commutators estimates and Bony’s decomposition.In Chapter 4,we investigate the norm inflation phenomenon of the Cauchy problem to the multidimensional compressible liquid-gas two-phase flow model.We prove the ill-posedness of the model in the sense that there is a so called norm inflation when the initial data belongs to some critical Besov spaces.The proof relies heavily on particular structure of the certain initial velocity₀,which induces a norm inflation happens in infinite time.In Chapter 5,the main results of the full paper are summarized and we present the relevant questions and research dierction in the future.