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2 results on '"Pierre Germain"'

1. Backward self-similar solutions for compressible Navier–Stokes equations

Author

Pierre Germain, Tristan Léger, and Tsukasa Iwabuchi

Subjects
Conjecture, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Symmetry in biology, General Physics and Astronomy, Statistical and Nonlinear Physics, 01 natural sciences, 010101 applied mathematics, Compressibility, 0101 mathematics, Compressible navier stokes equations, Mathematical Physics, Mathematics
Abstract

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.

Published
2021

2. An extension of the Derrida–Lebowitz–Speer–Spohn equation.

Author

Charles Bordenave, Pierre Germain, and Thomas Trogdon

Subjects
*EQUATIONS, *NUMERICAL analysis, *ALGEBRA, *MATHEMATICS, *MATHEMATICAL analysis
Abstract

We show how the derivation of the Derrida–Lebowitz–Speer–Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the paper by these authors. We then investigate its properties from both an analytical and numerical perspective. Specifically, a numerical method is presented to approximate solutions of the prolonged equation. Using this method, we investigate the relationship between the solutions of the prolonged equation and the Tracy–Widom GOE distribution. [ABSTRACT FROM AUTHOR]

Published
2015
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