We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension.Under the physical kinetic and dynamic conditions proposed on the free boundary,we investi...We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension.Under the physical kinetic and dynamic conditions proposed on the free boundary,we investigate the regularity of classical solutions to viscoelastic fluid equations in Sobolev spaces which are uniform in viscosity and justify the corresponding vanishing viscosity limits.The key ingredient of our proof is that the deformation gradient tensor in Lagrangian coordinates can be represented as a parameter in terms of the flow map so that the inherent structure of the elastic term improves the uniform regularity of normal derivatives in the limit of vanishing viscosity.This result indicates that the boundary layer does not appear in the free boundary problem of compressible viscoelastic fluids,which is different from the case studied by Mei et al.(2018)for the free boundary compressible Navier-Stokes system.展开更多
In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic ca...In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic case, we introduce a modified cut-off system depending on the conservative forces which needs the varied Bers skill, and construct the solution by the new variational formula. Moreover, comparing with previous results, our result extends the pressure-density relation to the general case. Afterwards we obtain the subsonic-sonic limit solution by taking the extract subsonic solutions as the approximate sequences.展开更多
基金supported by National Natural Science Foundation of China (Grant No.12031006)the Shanghai Frontier Research Center of Modern Analysis+1 种基金supported by National Natural Science Foundation of China (Grant No.12101496)the Fundamental Research Funds for the Central Universities (Grant No.G2021KY05101)。
文摘We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension.Under the physical kinetic and dynamic conditions proposed on the free boundary,we investigate the regularity of classical solutions to viscoelastic fluid equations in Sobolev spaces which are uniform in viscosity and justify the corresponding vanishing viscosity limits.The key ingredient of our proof is that the deformation gradient tensor in Lagrangian coordinates can be represented as a parameter in terms of the flow map so that the inherent structure of the elastic term improves the uniform regularity of normal derivatives in the limit of vanishing viscosity.This result indicates that the boundary layer does not appear in the free boundary problem of compressible viscoelastic fluids,which is different from the case studied by Mei et al.(2018)for the free boundary compressible Navier-Stokes system.
基金The research of Xumin Gu was supported in part by NSF of China under Grant 12031006The research of Tian-Yi Wang was supported in part by NSF of China under Grant 11971024 and 12061080。
文摘In this paper, we study the irrotational subsonic and subsonic-sonic fows with general conservative forces in the exterior domains. The conservative forces indicate the new Bernoulli law naturally. For the subsonic case, we introduce a modified cut-off system depending on the conservative forces which needs the varied Bers skill, and construct the solution by the new variational formula. Moreover, comparing with previous results, our result extends the pressure-density relation to the general case. Afterwards we obtain the subsonic-sonic limit solution by taking the extract subsonic solutions as the approximate sequences.
