scholarly journals KPZ equation tails for general initial data

2020 ◽  
Vol 25 (0) ◽  
Author(s):  
Ivan Corwin ◽  
Promit Ghosal
Keyword(s):  
Initial Data ◽  
Kpz Equation ◽  
General Initial Data

scholarly journals Constructions of L∞ Algebras and Their Field Theory Realizations

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Olaf Hohm ◽  
Vladislav Kupriyanov ◽  
Dieter Lüst ◽  
Matthias Traube
Keyword(s):  
Field Theory ◽  
Initial Data ◽  
Vector Space ◽  
Jacobi Identity ◽  
General Theorem ◽  
Commutator Algebra ◽  
Courant Algebroid ◽  
Linear Map ◽  
General Initial Data ◽  
Special Cases

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.

QUASINEUTRAL LIMIT OF THE DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS WITH GENERAL INITIAL DATA

2003 ◽  
Vol 13 (04) ◽  
pp. 463-470 ◽  
Author(s):  
CHRISTIAN SCHMEISER ◽  
SHU WANG
Keyword(s):  
Initial Data ◽  
Diffusion Model ◽  
Debye Length ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Uniform Estimates ◽  
Initial Layer ◽  
General Initial Data ◽  
Entropy Functionals ◽  
Quasineutral Limit

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.

scholarly journals On the Existence of Long-Time Classical Solutions for the 2D Inviscid Boussinesq Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiafa Xu ◽  
Lishan Liu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Life Span ◽  
Boussinesq Equations ◽  
Classical Solutions ◽  
Buoyancy Frequency ◽  
General Initial Data ◽  
The Cauchy Problem ◽  
Long Time

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 .

scholarly journals Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3145
Author(s):  
Divyang G. Bhimani ◽  
Saikatul Haque
Keyword(s):  
Initial Data ◽  
Modulation Spaces ◽  
Well Posedness ◽  
Wiener Amalgam Spaces ◽  
General Initial Data ◽  
Amalgam Spaces ◽  
Loss Of Regularity ◽  
Bbm Equation

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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