On the ill-posedness of active scalar equations with odd singular kernels

2016 ◽  
Author(s):  
Igor Kukavica ◽  
Vlad Vicol ◽  
Fei Wang
Keyword(s):  
Singular Kernels ◽  
Active Scalar Equations ◽  
Scalar Equations ◽  
Active Scalar

Martingale solutions for stochastic active scalar equations perturbed by non-trace class noise

2014 ◽  
Vol 17 (02) ◽  
pp. 1450010 ◽  
Author(s):  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
White Noise ◽  
Multiplicative Noise ◽  
Trace Class ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Class Noise ◽  
Active Scalar Equations ◽  
Scalar Equations ◽  
Martingale Solutions ◽  
Active Scalar

In this paper we prove the existence of martingale solutions for the 2D stochastic fractional vorticity Navier–Stokes equation driven by space-time white noise for α ∈ (½, 1] and the 2D stochastic quasi-geostrophic equation on 𝕋2 for α ∈ (0, 1] driven by non-trace class noise. We also cover the case driven by non-trace class multiplicative noise for all α ∈ (0, 1].

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