本文主要考虑了在三维空间中,带有滑移边界条件的Navier-Stokes/Allen-Cahn (NSAC)系统稳态弱解的存在性问题。通过运用Helmholtz速度分解定理、弱收敛极限和有效粘性通量的方法,证明了该系统在滑移边界条件下稳态弱解的存在性。In this...本文主要考虑了在三维空间中,带有滑移边界条件的Navier-Stokes/Allen-Cahn (NSAC)系统稳态弱解的存在性问题。通过运用Helmholtz速度分解定理、弱收敛极限和有效粘性通量的方法,证明了该系统在滑移边界条件下稳态弱解的存在性。In this paper, the existence of a steady-state weak solution for a Navier-Stokes/Allen-Cahn (NSAC) system with slip boundary conditions in 3D space is discussed. In this paper, the methods of Helmholtz’s velocity decomposition theorem, weak convergence limit and effective viscous flux are used to prove the existence of a steady-state weak solution under slip boundary conditions.展开更多
This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depen...This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.展开更多
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
文摘本文主要考虑了在三维空间中,带有滑移边界条件的Navier-Stokes/Allen-Cahn (NSAC)系统稳态弱解的存在性问题。通过运用Helmholtz速度分解定理、弱收敛极限和有效粘性通量的方法,证明了该系统在滑移边界条件下稳态弱解的存在性。In this paper, the existence of a steady-state weak solution for a Navier-Stokes/Allen-Cahn (NSAC) system with slip boundary conditions in 3D space is discussed. In this paper, the methods of Helmholtz’s velocity decomposition theorem, weak convergence limit and effective viscous flux are used to prove the existence of a steady-state weak solution under slip boundary conditions.
基金supported by the Key Project of the NSFC(12131010)the NSFC(11771155,12271032)+1 种基金the NSF of Guangdong Province(2021A1515010249,2021A1515010303)supported by the NSFC(11971179,12371205)。
文摘This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.
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.
