We prove the blow-up of the 3-D isentropic compressible Navier-Stokes equations for the adiabatic exponent $\lambda = 5/3$, which corresponds to the law of monatomic gas. This is the degenerate case in the sense of Merle-Raphaël-Rodnianski-Szeftel. This talk is based on a joint work with Shumao Wang, Dongyi Wei and Zhifei Zhang.

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/UCsGrCnMq5GW. Meeting code: 266-360-299. To join via a web browser: go to https://voovmeeting.com/; click "Log in" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 148-207-215 in the "Enter meeting ID" field; when prompted, select "Join from browser".

Currently, the mathematical model of an ideal three-layer incompressible fluid attracts considerable attention in the study of nonlinear internal waves [1–3]. This is due to the fact that, despite its relative simplicity, this model describes a fairly rich set of flow regimes that can be observed in nature and laboratory conditions. A special place among such regimes is occupied by a subclass of stratified flows described by the stationary equations of the second approximation of shallow water theory. Despite the large number of solutions of these equations obtained both analytically and numerically, the question of the qualitative behavior of wave structures in a three-layer flow remains insufficiently studied when its initial parameters are perturbed. In current report a procedure based on reducing the Hamilton's equations to normal form by canonical transformations uses for constructing asymptotic solutions. Thus, in the neighbourhood of the parameters corresponding to the bifurcation point, it is possible to describe second-mode soliton with undamped oscillations at infinity and classical first-mode soliton. Additionally, the analysis of the conditions under which the term corresponding to quadratic non-linearity vanishes in the asymptotic equations is carried out. In this case solutions such as fronts connecting a pair of conjugate states appear in the system.

The talk will be streamed through “Kontur Talk”: https://imsoran.ktalk.ru/ogsac0ijeetj