A Navier-Stokes-Voight model with memory

2013 ◽  
Vol 36 (18) ◽  
pp. 2507-2523 ◽  
Author(s):  
Ciprian G. Gal ◽  
T. Tachim Medjo
Keyword(s):  
Navier Stokes ◽  
With Memory

Local solvability of an inverse problem to the Navier–Stokes equation with memory term

2020 ◽  
Vol 36 (6) ◽  
pp. 065007
Author(s):  
Yu Jiang ◽  
Jishan Fan ◽  
Sei Nagayasu ◽  
Gen Nakamura
Keyword(s):  
Inverse Problem ◽  
Stokes Equation ◽  
Local Solvability ◽  
Navier Stokes ◽  
Memory Term ◽  
Navier Stokes Equation ◽  
With Memory

STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2005 ◽  
Vol 07 (05) ◽  
pp. 553-582 ◽  
Author(s):  
YURI BAKHTIN ◽  
JONATHAN C. MATTINGLY
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stationary Solution ◽  
Landau Equation ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Partial Differential ◽  
Navier Stokes Equation ◽  
With Memory

We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier–Stokes equation and stochastic Ginsburg–Landau equation.

scholarly journals Navier–Stokes–Voigt Equations with Memory in 3D Lacking Instantaneous Kinematic Viscosity

2017 ◽  
Vol 28 (2) ◽  
pp. 653-686 ◽  
Author(s):  
Francesco Di Plinio ◽  
Andrea Giorgini ◽  
Vittorino Pata ◽  
Roger Temam
Keyword(s):  
Kinematic Viscosity ◽  
Navier Stokes ◽  
With Memory

scholarly journals Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces

2021 ◽  
Vol 10 (1) ◽  
pp. 1-23
Author(s):  
Cung The Anh ◽  
◽  
Dang Thi Phuong Thanh ◽  
Nguyen Duong Toan ◽  
◽  
...  
Keyword(s):  
Navier Stokes ◽  
Uniform Attractors ◽  
External Forces ◽  
With Memory

scholarly journals Stability of stochastic 2D Navier-Stokes equations with memory and Poisson jumps

2020 ◽  
Vol 4 (1) ◽  
pp. 417-429
Author(s):  
Diem Dang Huan ◽  
Keyword(s):  
Hilbert Spaces ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mean Square ◽  
Stochastic Evolution ◽  
Poisson Jumps ◽  
Navier Stokes Equations ◽  
Stoke Equation ◽  
The Stability ◽  
With Memory

The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.

scholarly journals On Strong Solutions of Regularized Model of a Viscoelastic Medium with Variable Boundary

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Vladimir Orlov
Keyword(s):  
Viscoelastic Medium ◽  
Stokes System ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Systems Of Equations ◽  
Initial Value ◽  
Planar Case ◽  
Variable Boundary ◽  
With Memory ◽  
Regularized Model

We consider the initial-value problem for systems of equations describing the evolution of a viscoelastic medium with variable boundary with memory along the trajectories of a velocity field, which generalizes the Navier-Stokes system of equations. Nonlocal existence and uniqueness theorem of strong solutions containing senior square-integrable derivatives in the planar case are established.

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