|
|
| |
| Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System* |
| |
Citation： |
Song JIANG,Xiangxiang SU,Feng XIE.Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System*[J].Chinese Annals of Mathematics B,2023,44(5):663~686 |
| Page view： 1024
Net amount： 612 |
Authors： |
Song JIANG; Xiangxiang SU;Feng XIE |
Foundation： |
National Natural Science Foundation of China (Nos. 12271359,11831003, 12161141004, 11631008), Shanghai Science and Technology Innovation Action Plan (No. 20JC1413000), the National Key R&D Program (No. 2020YFA0712200), the National Key Project (No. GJXM92579), the Sino-German Science Center (No. GZ 1465) and the ISF-NSFC Joint Research Program (No. 11761141008). |
|
|
| Abstract： |
The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper. When the thickness of the diffuse interfacial zone, which is parameterized by ε, goes to zero, they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L∞(L2) ∩ L2(H1) sense on a uniform time interval independent of the small parameter ε. The proof consists of two parts: One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev spaces. Besides the careful energy estimates, a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error functions. The convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak. |
Keywords： |
Sharp interface limit, Incompressible Navier-Stokes equations, AllenCahn equation, Spectral estimate, Energy estimates |
Classification： |
35Q35, 35Q30, 76D05, 35R35 |
|
|
Download PDF Full-Text
|
|
|
|
