On the uniqueness of the solution of the flow problem with a given vortex

Weigant, W.; Papin, A. A.

doi:10.1134/s0001434614110248

Cited by 7 publications

(14 citation statements)

References 3 publications

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“…Solvability of initial-boundary value problems for the Euler equations and unsteady equation of a thin plate were studied in detail separately [11][12][13][14][15][16]. Initial-boundary value problems for unsteady Euler equations of a potential flow of a homogeneous liquid with a free surface were considered in detail [11].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Solvability of initial-boundary value problems for the Euler equations with a free surface was considered [12]. Uniqueness of the solution of the flow problem with a given vortex for the unsteady Euler equations of an ideal incompressible fluid was proved [13]. Equation (5) determines oscillations of a thin plate within the Kirchhoff-Love hypothesis of the linear theory of elasticity [17].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In this paper we study the uniqueness of the solution of the joint problem of a plate bending and motion of an ideal fluid. In order to prove the Theorem 1 we used approaches developed before [13].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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Uniqueness of a Solution of an Ice Plate Oscillation Problem in a Channel

Shishmarev¹,

Papin²

2018

J. Sib. Fed. Univ., Math. phys.

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In this paper an initial-boundary value problem for two mathematical models of elastic and viscoelastic oscillations of a thin ice plate in an infinite channel under the action of external load is considered in terms of the linear theory of hydroelasticity. The viscosity of ice is treated in the context of the Kelvin-Voigt model. The joint system of equations for the ice plate and an ideal fluid is considered. Boundary conditions are conditions of clamped edges for the ice plate at the walls of the channel, condition of impermeability for the flow velocity potential and the damping conditions for the oscillations at infinity. The uniqueness theorem for the classical solution of the initial-boundary value problem is proved.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

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Uniqueness of a Solution of an Ice Plate Oscillation Problem in a Channel

Shishmarev¹,

Papin²

2018

J. Sib. Fed. Univ., Math. phys.

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“…Разрешимость начально-краевых задач для уравнений Эйлера и динамики тонкой пласти-ны подробно исследованы по отдельности [14][15][16].…”

Section: искомыми являются функции ϕ(X Y Z T) W(x Y T)unclassified

“…Единственность решения в задаче протекания с заданным вихрем для нестационарных уравне-ний Эйлера идеальной несжимаемой жидкости доказана в работе [14]. Корректность начально-краевых задач для уравнения колебаний балки ис-следована в [17,18].…”

Section: искомыми являются функции ϕ(X Y Z T) W(x Y T)unclassified