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.

Large-frequency global regularity for the incompressible Navier–Stokes equation

1999 ◽  
Vol 129 (5) ◽  
pp. 903-912
Author(s):  
Joel D. Avrin
Keyword(s):  
Boundary Conditions ◽  
Global Regularity ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Thin Domains ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Incompressible Navier Stokes Equation

We obtain global existence and regularity of strong solutions to the incompressible Navier–Stokes equations for a variety of boundary conditions in such a way that the initial and forcing data can be large in the high-frequency eigenspaces of the Stokes operator. We do not require that the domain be thin as in previous analyses. But in the case of thin domains (and zero Dirichlet boundary conditions) our results represent a further improvement and refinement of previous results obtained.

AN ALGEBRAIC QUANTUM DYNAMICS INVESTIGATION OF PARTICLE TRANSPORT IN A QUANTUM RING

2012 ◽  
Vol 26 (09) ◽  
pp. 1250054
Author(s):  
H. PAHLAVANI ◽  
F. AREZOUMANDI
Keyword(s):  
Boundary Conditions ◽  
Quantum Dynamics ◽  
Dirichlet Boundary ◽  
Polynomial Algebra ◽  
Tight Binding ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Quantum Ring ◽  
Binding Model ◽  
Algebraic Quantum

The quantum dynamics of a driven single-band tight-binding model with infinite and Dirichlet boundary conditions is considered. The polynomial algebra for the above model but with periodic boundary conditions (quantum ring) is constructed. Based on analyzing the algebraic structures of Hamiltonian, the solution of the time-dependent Schrödinger equation is also obtained exactly.

scholarly journals Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain

2019 ◽  
Vol 18 (02) ◽  
pp. 211-235
Author(s):  
Michel Chipot ◽  
Jérôme Droniou ◽  
Gabriela Planas ◽  
James C. Robinson ◽  
Wei Xue
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Periodic Domain ◽  
Navier Stokes Equations ◽  
Forcing Function ◽  
Connected Set

We treat three problems on a two-dimensional “punctured periodic domain”: we take [Formula: see text], where [Formula: see text] and [Formula: see text] is the closure of an open connected set that is star-shaped with respect to [Formula: see text] and has a [Formula: see text] boundary. We impose periodic boundary conditions on the boundary of [Formula: see text], and Dirichlet boundary conditions on [Formula: see text]. In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier–Stokes equations, all with a fixed forcing function [Formula: see text], and examine the behavior of solutions as [Formula: see text]. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of [Formula: see text] with periodic boundary conditions.

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].

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