On the Boussinesq equations with non-monotone temperature profiles

DOI10.1007/s00332-021-09723-3zbMath1476.35270arXiv2011.02316OpenAlexW3164205638MaRDI QIDQ2043224

Christian Zillinger

Publication date: 29 July 2021

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.02316

zbMATH Keywords

Boussinesq equationsshear flowenhanced dissipationpartial dissipationhydrostatic imbalance

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Diffusive and convective heat and mass transfer, heat flow (80A19)

Related Items

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Uses Software

• DLMF

Cites Work

• Global well-posedness of the 2D Boussinesq equations with vertical dissipation
• On Landau damping
• Linear inviscid damping for Couette flow in stratified fluid
• Hydrodynamic instability and transition to turbulence
• Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
• The 2D Boussinesq equations with vertical viscosity and vertical diffusivity
• The Sobolev stability threshold for 2D shear flows near Couette
• Convergence to stratified flow for an inviscid 3D Boussinesq system
• Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion
• On the forced Euler and Navier-Stokes equations: linear damping and modified scattering
• On echo chains in Landau damping: traveling wave-like solutions and Gevrey 3 as a linear stability threshold
• On the Sobolev stability threshold of 3D Couette flow in a uniform magnetic field
• Nonlinear echoes and Landau damping with insufficient regularity
• Stability and decay rates for a variant of the 2D Boussinesq-Bénard system
• Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation
• Global regularity for the 2D Boussinesq equations with partial viscosity terms
• Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity
• On enhanced dissipation for the Boussinesq equations
• Sharp Decay Estimates for an Anisotropic Linear Semigroup and Applications to the Surface Quasi-Geostrophic and Inviscid Boussinesq Systems
• Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations
• On the smallness condition in linear inviscid damping: monotonicity and resonance chains

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