Remarks on global approximate controllability for the 2-D Navier–Stokes system with Dirichlet boundary conditions

2006 ◽  
Vol 343 (9) ◽  
pp. 573-577 ◽  
Author(s):  
Sergio Guerrero ◽  
Oleg Yurievich Imanuvilov ◽  
Jean-Pierre Puel
Keyword(s):  
Boundary Conditions ◽  
Approximate Controllability ◽  
Stokes System ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes

scholarly journals On a 2D stochastic Euler equation of transport type: Existence and geometric formulation

2014 ◽  
Vol 15 (01) ◽  
pp. 1450012 ◽  
Author(s):  
Ana Bela Cruzeiro ◽  
Iván Torrecilla
Keyword(s):  
Boundary Conditions ◽  
Euler Equation ◽  
Multiplicative Noise ◽  
Dirichlet Boundary ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Geometric Formulation ◽  
Transport Type

We prove weak existence of Euler equation (or Navier–Stokes equation) perturbed by a multiplicative noise on bounded domains of ℝ2 with Dirichlet boundary conditions and with periodic boundary conditions. Solutions are H1 regular. The equations are of transport type.

The resolvent problem for the Stokes system in exterior domains: uniqueness and non-regularity in Hölder spaces

1992 ◽  
Vol 122 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Paul Deuring
Keyword(s):  
Boundary Conditions ◽  
Existence Result ◽  
Stokes System ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Exterior Domains ◽  
Hölder Spaces ◽  
Image Position ◽  
Holder Spaces ◽  
Resolvent Problem

SynopsisWe consider the resolvent problem for the Stokes system in exterior domains, under Dirichlet boundary conditions:where Ω is a bounded domain in ℝ3. It will be shown that in general there is no constant C > 0 such that for with , div u = 0, and for with . However, if a solution (u, π) of problem (*) exists, it is uniquely determined, provided that u(x) and ∇π(x) decay for large values of |x|. These assertions imply a non-existence result in Hölder spaces.

scholarly journals Long-term behaviour in a chemotaxis-fluid system with logistic source

2016 ◽  
Vol 26 (11) ◽  
pp. 2071-2109 ◽  
Author(s):  
Johannes Lankeit
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Logistic Source ◽  
State Formula ◽  
Bounded Smooth ◽  
Homogeneous Dirichlet Boundary Conditions

We consider the coupled chemotaxis Navier–Stokes model with logistic source terms: [Formula: see text] [Formula: see text] [Formula: see text] in a bounded, smooth domain [Formula: see text] under homogeneous Neumann boundary conditions for [Formula: see text] and [Formula: see text] and homogeneous Dirichlet boundary conditions for [Formula: see text] and with given functions [Formula: see text] satisfying certain decay conditions and [Formula: see text] for some [Formula: see text]. We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state [Formula: see text].

Approximate controllability of semilinear impulsive strongly damped wave equation

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Hanzel Larez ◽  
Hugo Leiva ◽  
Jorge Rebaza ◽  
Addison Ríos
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Approximate Controllability ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

AbstractRothe's fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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