• Corpus ID: 119618951

Ergodicity of spherically symmetric fluid flows outside of a Schwarzschild black hole with random boundary forcing

  title={Ergodicity of spherically symmetric fluid flows outside of a Schwarzschild black hole with random boundary forcing},
  author={Yuri Bakhtin and Philippe G. LeFloch},
  journal={arXiv: Analysis of PDEs},
We consider the Burgers equation posed on the outer communication region of a Schwarzschild black hole spacetime. Assuming spherical symmetry for the fluid flow under consideration, we study the propagation and interaction of shock waves under the effect of random forcing. First of all, considering the initial and boundary value problem with boundary data prescribed in the vicinity of the horizon, we establish a generalization of the Hopf--Lax--Oleinik formula, which takes the curved geometry… 
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