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arXiv · 1904.06797

On a mixed problem for the parabolic Lam'e type operator

R. Puzyrev·A. Shlapunov
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Abstract

We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the parabolic Lam\'e type system in a cylindrical domain, via its values and the values of the boundary stress tensor on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding H\"older spaces; besides, additional initial data do not turn the problem to a well-posed one. Using the Integral Representation's Method we obtain the Uniqueness Theorem and solvability conditions for the problem.

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R. Puzyrev, A. Shlapunov. 2019-04-15. On a mixed problem for the parabolic Lam'e type operator. https://doi.org/10.1515/jiip-2014-0043

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