Existence of Solutions to the Nonstationary Stokes System with a Nonlinear Overdetermination Condition

In this paper, we study an inverse problem for the nonstationary Stokes system in a bounded domain Ω with a nonlinear integral overdetermination condition, describing the kinetic energy E(t) of the fluid. We construct two classes of solutions: weak and very weak. In the case where the kinetic energy E belongs to W21(0,T), we construct weak solutions. If E belongs only to L2(0,T), we construct very weak solutions.

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Publication Details

Journal
Mathematics
Published
2026-04-22
DOI
https://doi.org/10.3390/math14091402
Primary Topic
Stability and Controllability of Differential Equations
Type
article
Field-Weighted Citation Impact
0.00

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article

Existence of Solutions to the Nonstationary Stokes System with a Nonlinear Overdetermination Condition

Kristina Kaulakytė, Vytautas Bačianskas
Mathematics
Stability and Controllability of Differential Equations
article

Existence of Solutions to the Nonstationary Stokes System with a Nonlinear Overdetermination Condition

Kristina Kaulakytė, Vytautas Bačianskas
article en

Abstract

In this paper, we study an inverse problem for the nonstationary Stokes system in a bounded domain Ω with a nonlinear integral overdetermination condition, describing the kinetic energy E(t) of the fluid. We construct two classes of solutions: weak and very weak. In the case where the kinetic energy E belongs to W21(0,T), we construct weak solutions. If E belongs only to L2(0,T), we construct very weak solutions.

MathematicsVol. 14(9)
Vilnius University (LT)
Lietuvos Mokslo Taryba
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Stability and Controllability of Differential Equations
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Existence of Solutions to the Nonstationary Stokes System with a Nonlinear Overdetermination Condition — Kristina Kaulakytė, Vytautas Bačianskas · Mathematics (2026) | TGRS Research Map | TGRS