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On 2-dimensional stochastic sine Gordon equation

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Sosoe, Philippe

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On 2-dimensional stochastic sine Gordon equation
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On the two-dimensional hyperbolic sine-Gordon equation
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14
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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We study the two-dimensional stochastic sine-Gordon equation (SSG) in the hyperbolic setting. In particular, by introducing a suitable time-dependent renormalization, we prove local well- posedness of SSG for any value of a parameter \beta > 0 in the nonlinearity. This is in contrast to the parabolic case studied by Hairer and Shen (2016) and Chandra-Hairer-Shen (2018), where the parameter is restricted to the subcritical range \beta^2 < 8*pi.