scholarly journals KPZ equation tails for general initial data

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Ivan Corwin ◽  
Promit Ghosal

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Olaf Hohm ◽  
Vladislav Kupriyanov ◽  
Dieter Lüst ◽  
Matthias Traube

We construct L∞ algebras for general “initial data” given by a vector space equipped with an antisymmetric bracket not necessarily satisfying the Jacobi identity. We prove that any such bracket can be extended to a 2-term L∞ algebra on a graded vector space of twice the dimension, with the 3-bracket being related to the Jacobiator. While these L∞ algebras always exist, they generally do not realize a nontrivial symmetry in a field theory. In order to define L∞ algebras with genuine field theory realizations, we prove the significantly more general theorem that if the Jacobiator takes values in the image of any linear map that defines an ideal there is a 3-term L∞ algebra with a generally nontrivial 4-bracket. We discuss special cases such as the commutator algebra of octonions, its contraction to the “R-flux algebra,” and the Courant algebroid.



2003 ◽  
Vol 13 (04) ◽  
pp. 463-470 ◽  
Author(s):  
CHRISTIAN SCHMEISER ◽  
SHU WANG

The limit for vanishing Debye length (charge neutral limit) in a bipolar drift-diffusion model for semiconductors with general initial data allowing the presence of an initial layer is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using two different entropy functionals which yield appropriate uniform estimates. This investigation extends the results of Refs. 7 and 8 for charge neutral initial data where no initial layer occurs.



2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiafa Xu ◽  
Lishan Liu

In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. It is proved that for general initial data u 0 ∈ H s with s > 3 , the life span of the classical solutions satisfies T > C ln     N 3 / 4 .



Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3145
Author(s):  
Divyang G. Bhimani ◽  
Saikatul Haque

We consider the Benjamin–Bona–Mahony (BBM) equation of the form ut+ux+uux−uxxt=0,(x,t)∈M×R where M=T or R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and Wiener amalgam spaces with negative regularity. This strengthens several known NI results at zero initial data in Hs(T) established by Bona–Dai (2017) and the ill-posedness result established by Bona–Tzvetkov (2008) and Panthee (2011) in Hs(R). Our result is sharp with respect to the local well-posedness result of Banquet–Villamizar–Roa (2021) in modulation spaces Ms2,1(R) for s≥0.



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