# Backward self-similar solutions for compressible Navier–Stokes equations

@article{Germain2021BackwardSS, title={Backward self-similar solutions for compressible Navier–Stokes equations}, author={Pierre Germain and Tsukasa Iwabuchi and Tristan L{\'e}ger}, journal={Nonlinearity}, year={2021}, volume={34}, pages={868 - 893} }

This article is devoted to backward self-similar blow up solutions of the compressible Navier–Stokes equations with radial symmetry. We show that such solutions cannot exist if they either have finite energy, or satisfy appropriate smallness conditions. Furthermore, numerical simulations lead us to the conjecture that such solutions do not exist.

## One Citation

On Self-similar Solutions to Degenerate Compressible Navier–Stokes Equations

- Mathematics
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We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existence of small…

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