LOCAL EXISTENCE THEOREMS WITH UNBOUNDED SET OF INPUT DATA AND UNBOUNDEDNESS OF STABLE INVARIANT MANIFOLDS FOR 3D NAVIER-STOKES EQUATIONS

Andrei Fursikov

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LOCAL EXISTENCE THEOREMS WITH UNBOUNDED SET OF INPUT DATA AND UNBOUNDEDNESS OF STABLE INVARIANT MANIFOLDS FOR 3D NAVIER-STOKES EQUATIONS

机译：输入数据无界的局部存在定理和3D Navier-Stokes方程的稳定不变流形的无界性

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摘要

Local existence theorem of smooth solution v(t, ·),t∈R_+ for 3D Navier-Stokes equations is proved, when initial data belongs to a certain unbounded ellipsoid of suitable function space. Unboundedness of stable invariant manifolds for 3D Navier-Stokes equations is proved as well.

机译：当初始数据属于适当函数空间的某个无界椭球时，证明了3D Navier-Stokes方程的光滑解v（t，·），t∈R_+的局部存在性定理。并证明了3D Navier-Stokes方程稳定不变流形的无界性。

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《Discrete and continuous dynamical systems▼hSeries S》 |2010年第2期|P.269-289|共21页
作者
Andrei Fursikov;
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作者单位

Department of Mechanics & Mathematics, Moscow State University Moscow 119991, Russia;

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原文格式 PDF
正文语种 eng
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关键词
local existence theorem; unbounded input data; stable invariant manifold;

机译：局部存在定理无限制的输入数据;稳定不变流形;

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2. Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D domains [J] . Brze?niak Z., Motyl E. Journal of Differential Equations . 2013,第4期

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3. UNSTABLE INVARIANT MANIFOLDS FOR A NONAUTONOMOUS DIFFERENTIAL EQUATION WITH NONAUTONOMOUS UNBOUNDED DELAY [J] . Arne Ogrowsky, Bjorn Schmalfuss Discrete and continuous dynamical systems . 2013,第6期

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5. A spectral/B-spline method for the Navier-Stokes equations in unbounded cylindrical domains. [D] . Dufresne, Louis. 2001

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6. Local and global existence theorems for the Einstein equations [O] . Alan D. Rendall -1

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7. Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D-domains [O] . Brzeźniak, Zdzisław, Motyl, Elżbieta 2017

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8. Remarks on the Existence and Uniqueness of Unbounded Viscosity Solutions of Hamilton-Jacobi Equations [R] . Crandall, M. G., Lions, P. L. 1985

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LOCAL EXISTENCE THEOREMS WITH UNBOUNDED SET OF INPUT DATA AND UNBOUNDEDNESS OF STABLE INVARIANT MANIFOLDS FOR 3D NAVIER-STOKES EQUATIONS

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