Registered Data

[CT135]

  • Session Time & Room
  • Classification
    • CT135 (1/1) : Compressible fluids and gas dynamics, general (76N) / Reaction effects in flows (76V) / Turbulence (76F) / Waves in solid mechanics (74J)

[02054] Low regularity ill-posedness for elastic waves and ideal compressible MHD in 3D and 2D

  • Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817 A715
  • Type : Contributed Talk
  • Abstract : We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$, respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations, we reveal their hidden subtle structures. With them we give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. If time permits, we will also present the corresponding results in 2D. This talk is based on joint works with Haoyang Chen and Silu Yin.
  • Classification : 76N15, 76N30, 35L60, 35L67, 35Q35
  • Format : Talk at Waseda University
  • Author(s) :
    • Xinliang An (National University of Singapore)
    • Haoyang Chen (National University of Singapore)
    • Silu Yin (Hangzhou Normal University)

[01096] Stability modulation by a reaction in Navier-Stokes flow

[02142] Self-similar hierarchy of vortices in turbulence

  • Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817 A715
  • Type : Contributed Talk
  • Abstract : By direct numerical simulations, we show that there exists the hierarchy of vortex axes in turbulence, which is self-similar in a wide range of scales, i.e., in the inertial range and a lower part of the dissipation range. This result means that the volume fraction occupied by the tubular vortices at each scale is independent of the scale.
  • Classification : 76F65, 65Z05
  • Format : Talk at Waseda University
  • Author(s) :
    • Tomonori Tsuruhashi (The University of Tokyo)
    • Susumu Goto (Osaka University)
    • Sunao Oka (Osaka University)
    • Tsuyoshi Yoneda (Hitotsubashi University)

[01101] Supersonic Pre-Transitional Disturbances in Boundary Layers on Porous Surfaces

  • Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817 A715
  • Type : Contributed Talk
  • Abstract : The effect of wall permeability on the response of pre-transitional supersonic boundary layers subject to low-amplitude, free-stream vortical disturbances is investigated via asymptotic methods and numerically. Equally-spaced cylindrical pores couple the pressure and wall-normal velocity fluctuations when the spanwise diffusion is negligible, thereby reducing the growth of low-frequency laminar streaks and Görtler vortices on concave porous walls. Highly-oblique Tollmien-Schlichting waves that develop further downstream are instead enhanced. This finding is confirmed by a triple-deck analysis.
  • Classification : 76N20, 76N25, 35C20
  • Format : Talk at Waseda University
  • Author(s) :
    • Ludovico Fossà (The University of Sheffield)
    • Pierre Ricco (The University of Sheffield)

[01861] Scattering of an Ostrovsky wave packet in a layered waveguide

  • Session Time & Room : 5D (Aug.25, 15:30-17:10) @E817 A715
  • Type : Contributed Talk
  • Abstract : In this talk I will discuss the scattering of an Ostrovsky wave packet in a two layered waveguide with a delamination sandwiched between imperfect bonding. When the layers have different densities, the strains are described by a system of coupled Boussinesq equations. Asymptotic solutions are constructed, complemented by numerical simulations, and are used to analyse the scattering of the strain waves. These results can provide a tool to control the integrity of layered structures.
  • Classification : 74J30, 76B15, 35G25, 35G30
  • Format : Online Talk on Zoom
  • Author(s) :
    • Jagdeep Tamber (Nottingham Trent University)