Ajay Chandra, Léonard Ferdinand
Published 2024-02-05, updated 2024-02-19Version 2
We show that the flow approach of Duch [Duc21] can be adapted to prove local well-posedness for the generalised KPZ equation. The key step is to extend the flow approach so that it can accommodate semilinear equations involving smooth functions of the solution instead of only polynomials - this is accomplished by introducing coordinates for the flow built out of the elementary differentials associated to the equation.
Comments: Added a new argument for integrable covariances that allows colored noise in 2+1 dimensions. Made changes to allow for more terms in generalized KPZ equation. Many fixes of typos and notation
Rough differential equations in the flow approach
Local well-posedness of Musiela's SPDE with Lévy noise
Stochastic complex Ginzburg-Landau equation with space-time white noise
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