Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces
نویسندگان
چکیده
Abstract Uniqueness of Leray solutions the 3D Navier-Stokes equations is a challenging open problem. In this article we will study problem for stationary in whole space R 3 . Under some additional hypotheses, stated terms Lebesgue and Morrey spaces, show that trivial solution U ? = 0 unique solution. This type results are known as Liouville theorems.
منابع مشابه
Liouville Theorem for 2d Navier-stokes Equations
(One may modify the question by putting various other restrictions on (L); for example, one can consider only steady-state solutions, or solutions with finite rate of dissipation or belonging to various other function spaces, etc.) We have proved a positive result for dimension n = 2 which we will discuss below, but let us begin by mentioning why the basic problem is interesting. Generally spea...
متن کاملLiouville type of theorems with weights for the Navier-Stokes equations and the Euler equations
We study Liouville type of theorems for the Navier-Stokes and the Euler equations on R N , N ≥ 2. Specifically, we prove that if a weak solution (v, p) satisfies |v| 2 +|p| ∈ L 1 (0, T ; L 1 (R N , w 1 (x)dx)) and R N p(x, t)w 2 (x)dx ≥ 0 for some weight functions w 1 (x) and w 2 (x), then the solution is trivial, namely v = 0 almost everywhere on R N × (0, T). Similar results hold for the MHD ...
متن کاملThe Stationary Navier-Stokes Equations
Having considered the linear Stokes equations, we will now bring back the nonlinear term and consider the nonlinear version of the Stokes system. The solution of these equations can be viewed as the limit to which the solution of the full N-S equations tends as t tends to infinity. Of course no one knows at this point if the solutions of the N-S equations do tend to some limit as t tends to inf...
متن کاملRegularity for Suitable Weak Solutions to the Navier-Stokes Equations in Critical Morrey Spaces
A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are invariant with respect to the Navier-Stokes equations scaling. The famous Caffarelli-Kohn-Nirenberg condition is contained in that class as a particular case. 1991...
متن کاملLiouville type of theorems for the Euler and the Navier-Stokes equations
We prove Liouville type of theorems for weak solutions of the Navier-Stokes and the Euler equations. In particular, if the pressure satisfies p ∈ L1(0, T ;H1(RN )), then the corresponding velocity should be trivial, namely v = 0 on RN × (0, T ), while if p ∈ L1(0, T ;L1(RN )), then we have equipartition of energy over each component. Similar results hold also for the magnetohydrodynamic equations.
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: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2021
ISSN: ['0294-1449', '1873-1430']
DOI: https://doi.org/10.1016/j.anihpc.2020.08.006