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Journal of Mathematical Sciences

, Volume 238, Issue 5, pp 652–657 | Cite as

Weak Solutions of Hopf Type to 2D Maxwell Flows with Infinite Number of Relaxation Times

  • N. A. KarazeevaEmail author
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A system of equations describing the motion of fluids of Maxwell type is considered:
$$ \frac{\partial }{\partial t}\upsilon +\upsilon \cdot \nabla \upsilon -\underset{0}{\overset{t}{\int }}K\left(t-\tau \right) d\tau +\nabla p=f\left(x,t\right),\kern0.5em di\upsilon\;\upsilon =0. $$
Here K(t) is an exponential series \( K(t)=\sum \limits_{s=1}^{\infty }{\beta}_s{e}^{-{\alpha}_st} \). The existence of a weak solution for the initial boundary value problem
$$ {\left.\begin{array}{ccc}\upsilon \left(x,0\right)={\upsilon}_0(x),& {\left.\upsilon \cdot n\right|}_{\partial \varOmega }=0,& rot\end{array}\;\upsilon \right|}_{\partial \varOmega }=0 $$

is proved.

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Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical Institute, RASSt. PetersburgRussia

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