Well-posedness of the free boundary problem in incompressible elastodynamics
نویسندگان
چکیده
منابع مشابه
Well-posedness for the Linearized Motion of an Incompressible Liquid with Free Surface Boundary
Condition (1.3) says that the pressure p vanishes outside the domain and condition (1.4) says that the boundary moves with the velocity V of the fluid particles at the boundary. Given a domain D0 ⊂ R, that is homeomorphic to the unit ball, and initial data v0, satisfying the constraint (1.2), we want to find a set D = ∪ 0≤t≤T {t} × Dt, Dt ⊂ R and a vector field v solving (1.1)-(1.4) with initia...
متن کاملWell-posedness for the Motion of an Incompressible Liquid with Free Surface Boundary
Abstract. We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler’s equations, where the regularity of the boundary enters to highest order. We prove local ex...
متن کاملOn well-posedness for a free boundary fluid-structure model
Related Articles Generalized extended Navier-Stokes theory: Correlations in molecular fluids with intrinsic angular momentum J. Chem. Phys. 138, 034503 (2013) Velocity relaxation of an ellipsoid immersed in a viscous incompressible fluid Phys. Fluids 25, 013101 (2013) Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems J. Math. Phys. 54, 011502 (2013) Germano identit...
متن کاملWell-posedness of the Free-surface Incompressible Euler Equations with or without Surface Tension
We develop a new methodology for treating free boundary problems in mechanics, and use it to prove local-in-time well-posedness in Sobolev spaces for the freesurface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liqu...
متن کاملA Simple Proof of Well-posedness for the Free-surface Incompressible Euler Equations
The purpose of this this paper is to present a new simple proof for the construction of unique solutions to the moving free-boundary incompressible 3-D Euler equations in vacuum. Our method relies on the Lagrangian representation of the fluid, and the anisotropic smoothing operation that we call horizontal convolution-by-layers. The method is general and can be applied to a number of other movi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2019
ISSN: 0022-0396
DOI: 10.1016/j.jde.2019.07.001