Smooth imploding solutions for 3D compressible fluids

"Smooth imploding solutions for 3D compressible fluids", organizado polo CITMAga en formato híbrido, presencial e en liña. Será impartido por Gonzalo Cao Labora (Massachusetts Institute of Technology)

Data: martes 28 de marzo

Hora: 12:00 h.

Lugar: Aula magna, Facultade de Matemáticas da USC e tamén en liña (MS Teams)

Abstract:

We will talk about singularity formation for the 3D compressible Euler and Navier-Stokes equations for ideal gases. These equations describe the motion of a compressible ideal gas, which is characterized by a parameter called adiabatic constant. Finite time singularities for generic adiabatic constants were found in the recent works of Merle, Raphaël, Rodnianski and Szeftel [2, 3], based on a stability argument around self-similar profiles.
We will construct a new family of profiles for all values of the adiabatic constant, providing the first singularity formation result for monoatomic gases (adiabatic constant equal to 5/3) [1]. We will also perform a new stability analysis to obtain the first singularities with nonvanishing density [1]. These results combine tools from PDE, dynamical systems and computer-assisted proofs, but the talk will be available to a general audience within mathematics.

References:
[1] T. Buckmaster, G. Cao-Labora, J. Gómez-Serrano arXiv preprint 2208.09445
[2] F. Merle, P. Raphaël, I. Rodnianski, J. Szeftel. On the implosion of a compressible fluid I: Smooth self-similar inviscid profiles. Annals of Mathematics 196 (2022), 567-778.
[3] F. Merle, P. Raphaël, I. Rodnianski, J. Szeftel. On the implosion of a compressible fluid II: Singularity formation. Annals of Mathematics 196 (2022), 779-889.