具有记忆的粘弹性连续体非齐次动力问题的弱可解性

Pub Date : 2023-09-05 DOI:10.1134/S0016266323010082
V. G. Zvyagin, V. P. Orlov
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引用次数: 0

摘要

证明了具有记忆的粘弹性流体沿非光滑速度场非齐次边界条件运动方程初边值问题弱解的存在性。分析涉及到原始问题的伽辽金型近似,然后通过基于先验估计的极限。为了研究非光滑速度场的轨迹行为,应用了正则拉格朗日流动理论。
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The Weak Solvability of an Inhomogeneous Dynamic Problem for a Viscoelastic Continuum with Memory

The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used.

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