Global solutions to a reactive Boussinesq system with front data on an infinite domain

Simon Malham Jack Xin

Analysis of PDEs mathscidoc:1912.43856

Communications in mathematical physics, 193, (2), 287-316, 1998.4
We prove the existence of global solutions to a coupled system of NavierStokes, and reaction-diffusion equations (for temperature and mass fraction) with prescribed front data on an infinite vertical strip or tube. This system models a one-step exothermic chemical reaction. The heat release induced volume expansion is accounted for via the Boussinesq approximation. The solutions are time dependent moving fronts in the presence of fluid convection. In the general setting, the fronts are subject to intensive Rayleigh-Taylor and thermal-diffusive instabilities. Various physical quantities, such as fluid velocity, temperature, and front speed, can grow in time. We show that the growth is at most for large time <i>t</i> by constructing a nonlinear functional on the temperature and mass fraction components. These results hold for arbitrary order reactions in two space dimensions and for quadratic and cubic reactions in
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@inproceedings{simon1998global,
  title={Global solutions to a reactive Boussinesq system with front data on an infinite domain},
  author={Simon Malham, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210231893156420},
  booktitle={Communications in mathematical physics},
  volume={193},
  number={2},
  pages={287-316},
  year={1998},
}
Simon Malham, and Jack Xin. Global solutions to a reactive Boussinesq system with front data on an infinite domain. 1998. Vol. 193. In Communications in mathematical physics. pp.287-316. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210231893156420.
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