scholarly journals Singular initial data and uniform global bounds for the hyper-viscous Navier–Stokes equation with periodic boundary conditions

2003 ◽  
Vol 190 (1) ◽  
pp. 330-351 ◽  
Author(s):  
Joel Avrin
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Stokes Equation ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Singular Initial Data

scholarly journals Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

2013 ◽  
Vol 45 (3) ◽  
pp. 742-772
Author(s):  
G. N. Milstein ◽  
M. V. Tretyakov
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Weak Sense ◽  
Periodic Boundary Conditions ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Probabilistic Nature

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

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.

On the Navier-Stokes equation with boundary conditions based on vorticity

2004 ◽  
Vol 269-270 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Hamid Bellout ◽  
Jiří Neustupa ◽  
Patrick Penel
Keyword(s):  
Boundary Conditions ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation
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