scholarly journals Global well-posedness and symmetries for dissipative active scalar equations with positive-order couplings

2016 ◽  
Vol 60 ◽  
pp. 525-550
Author(s):  
L. C. F. Ferreira ◽  
L. S. M. Lima
Keyword(s):  
Well Posedness ◽  
Positive Order ◽  
Active Scalar Equations ◽  
Scalar Equations ◽  
Active Scalar

scholarly journals Global well-posedness of slightly supercritical active scalar equations

2014 ◽  
Vol 7 (1) ◽  
pp. 43-72 ◽  
Author(s):  
Michael Dabkowski ◽  
Alexander Kiselev ◽  
Luis Silvestre ◽  
Vlad Vicol
Keyword(s):  
Well Posedness ◽  
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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