Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl
نویسندگان
چکیده
We study the asymptotic behavior of axisymmetric solutions with no swirl to steady Navier-Stokes equations in outside cylinder. prove an a priori decay estimate vorticity under assumption that velocity has generalized finite Dirichlet integral. As application, we obtain Liouville-type theorem.
منابع مشابه
3d Steady Compressible Navier–stokes Equations
2000 Mathematics Subject Classification. Primary: 76N10; Secondary: 35Q30.
متن کاملAxisymmetric Solutions to Coupled Navier-Stokes/Allen-Cahn Equations
We investigate a family of axisymmetric solutions to a coupling of Navier-Stokes and Allen-Cahn equations in R3. Firstly, a 1D system of equations is derived from the method of separation of variables, which approximates the 3D system along its symmetry axis. Then based on them, by adding perturbation terms, we construct finite energy solutions to the 3D system. We prove the global regularity o...
متن کاملDynamic Stability of the Three-Dimensional Axisymmetric Navier-Stokes Equations with Swirl
In this paper, we study the dynamic stability of the three-dimensional axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional model that approximates the Navier-Stokes equations along the symmetry axis. An important property of this one-dimensional model is that one can construct from its solutions a family of exact solutions of the threedimensionaFin...
متن کاملHomogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions
We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles, parameterizing them as a four dimensional surface with boundary in appropriate function spaces. Then we establish smoothness properties of the solution surface in the four parameters. The smo...
متن کاملSmooth Solutions to the 3D Navier-Stokes Equations Exist
In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the existence and uniqueness of smooth solutions to the 3D Navier-Stokes equations with periodic boundary conditions using the same strategy. In this paper, we mo...
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 Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2021.109289