Well Posedness and Asymptotic Expansion of Solution of Stokes Equation Set in a Thin Cylindrical Elastic Tube

2009 ◽  
pp. 275-301 ◽  
Author(s):  
Grigory P. Panasenko ◽  
Ruxandra Stavre
Keyword(s):  
Asymptotic Expansion ◽  
Stokes Equation ◽  
Elastic Tube ◽  
Well Posedness ◽  
Asymptotic Expansion Of Solution

scholarly journals Addendum to “The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation”

2013 ◽  
Vol 23 (4) ◽  
pp. 905-906
Author(s):  
Alexander Khapalov
Keyword(s):  
Incompressible Fluid ◽  
Stokes Equation ◽  
Well Posedness

Abstract In this addendum we address some unintentional omission in the description of the swimming model in our recent paper (Khapalov, 2013)

scholarly journals On a Nonlinear Wave Equation of Kirchhoff-Carrier Type: Linear Approximation and Asymptotic Expansion of Solution in a Small Parameter

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Nguyen Huu Nhan ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Weak Solution ◽  
Dirichlet Problem ◽  
Small Parameter ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Existence And Uniqueness ◽  
Linearization Method ◽  
Asymptotic Expansion Of Solution

We consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type. Using the Faedo-Galerkin method and the linearization method for nonlinear terms, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.

scholarly journals ASYMPTOTIC EXPANSION OF SOLUTION OF GENERAL BVP WITH INITIAL JUMPS FOR HIGHER-ORDER SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATION

2018 ◽  
pp. 28-36
Author(s):  
Dauylbayev M. ◽  
Atakhan N. ◽  
Mirzakulova A.E.
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Higher Order ◽  
Singularly Perturbed ◽  
Jump Phenomenon ◽  
Integro Differential Equation ◽  
Asymptotic Expansion Of Solution ◽  
Initial Jump

In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.

scholarly journals The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation

2013 ◽  
Vol 23 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Alexander Khapalov
Keyword(s):  
Incompressible Fluid ◽  
Stokes Equation ◽  
Reynolds Numbers ◽  
The Self ◽  
Well Posedness ◽  
Propulsion Systems ◽  
Engineering Applications ◽  
Low Reynolds Numbers ◽  
Low Reynolds

We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer’s body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids.

scholarly journals Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Eduardo Renteria Casas
Keyword(s):  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Arbitrary Dimensions ◽  
Parameter Ranges

Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \bWmop)$ for $p$ and $q$ in  appropriate parameter ranges are proven. The case of spatially measured-valued inhomogeneities is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions with $1 < p, q < \infty$ arbitrary.

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