Regularity results for viscous 3D Boussinesq temperature fronts
arXiv:1809.00701 · doi:10.1007/s00220-020-03767-4
Abstract
This paper is about the dynamics of non-diffusive temperature fronts evolving by the incompressible viscous Boussinesq system in . We provide local in time existence results for initial data of arbitrary size. Furthermore, we show global in time propagation of regularity for small initial data in critical spaces. The developed techniques allow to consider general fronts where the temperature is piecewise Hölder (not necessarily constant), which preserve their structure together with the regularity of the evolving interface.
References in corpus (11)
- Potentially Singular Solutions of the 3D Incompressible Euler Equations
- Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
- Global well-posedness of the 2D Boussinesq equations with vertical dissipation
- Absence of splash singularities for SQG sharp fronts and the Muskat problem
- Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems
- Finite time blow up for a 1D model of 2D Boussinesq system
- On the absence of "splash" singularities in the case of two-fluid interfaces
- Convergence to Stratified Flow for an Inviscid 3D Boussinesq System
- Absence of squirt singularities for the multi-phase Muskat problem
- Finite-time Singularity Formation for Strong Solutions to the Boussinesq System
- Finite time blow up in the hyperbolic Boussinesq system