PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES

@article{Gubinelli2012PARACONTROLLEDDA,
  title={PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES},
  author={Massimiliano Gubinelli and Peter Imkeller and Nicolas Perkowski},
  journal={Forum of Mathematics, Pi},
  year={2012},
  volume={3}
}
We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems such as differential equations driven by fractional Brownian motion, a fractional Burgers-type stochastic PDE (SPDE) driven by space-time white noise, and a nonlinear version of the parabolic Anderson model with a white noise potential. 

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