This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy...This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.展开更多
The first modern Olympic Games took place in Athens in 1896.While in those early days of the Olympics only amateur and gentleman athletes were allowed to participate,today Olympic athletes are highly trained professio...The first modern Olympic Games took place in Athens in 1896.While in those early days of the Olympics only amateur and gentleman athletes were allowed to participate,today Olympic athletes are highly trained professionals often dedicating decades of preparation for the chance to compete in the Olympic Games.In sharp contrast to these highly trained athletes,the world’s population becomes less physically active on average,resulting in an obesity epidemic with associated metabolic syndrome and increased mortality through non-communicable diseases(e.g.,Collins et al.^(1)).展开更多
基金National Natural Science Foundation of China(No.61675096)Fundamental Research Funds for the Centre Universities(No.30922010801)+1 种基金Fundamental Research Funds for NUST(No.TSXK2022D006)Postgraduate Research Practice Innovation Program of Jiangsu Province(No.KYCX23_0442)。
基金supported by the National Natural Science Foundation of China(12361044)supported by the National Natural Science Foundation of China(12171024,11971217,11971020)supported by the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027)。
文摘This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.
文摘The first modern Olympic Games took place in Athens in 1896.While in those early days of the Olympics only amateur and gentleman athletes were allowed to participate,today Olympic athletes are highly trained professionals often dedicating decades of preparation for the chance to compete in the Olympic Games.In sharp contrast to these highly trained athletes,the world’s population becomes less physically active on average,resulting in an obesity epidemic with associated metabolic syndrome and increased mortality through non-communicable diseases(e.g.,Collins et al.^(1)).
