Non relativistic and ultra relativistic limits in 2d stochastic nonlinear damped Klein-Gordon equation

1 Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan; fukuizumi@math.is.tohoku.ac.jp 2 Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531,Japan; hoshino@sigmath.es.osaka-u.ac.jp 3 Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; inui@math.sci.osaka-u.ac.jp

[1]  L. Cugliandolo,et al.  Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle. , 2016, Physical review. E.

[2]  Kenji Nakanishi,et al.  Invariant Manifolds and Dispersive Hamiltonian Evolution Equations , 2011 .

[3]  Takahisa Inui,et al.  Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation , 2021, Journal of Hyperbolic Differential Equations.

[4]  L. Tolomeo Unique Ergodicity for a Class of Stochastic Hyperbolic Equations with Additive Space-Time White Noise , 2018, 1811.06294.

[5]  Mark Freidlin,et al.  On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom , 2006 .

[6]  Martin Hairer,et al.  Triviality of the 2D stochastic Allen-Cahn equation , 2012, 1201.3089.

[7]  Justin Forlano,et al.  On the unique ergodicity for a class of 2 dimensional stochastic wave equations , 2021 .

[8]  Tadahiro Oh,et al.  A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations , 2015, Stochastics and Partial Differential Equations: Analysis and Computations.

[9]  G. Prato,et al.  Strong solutions to the stochastic quantization equations , 2003 .

[10]  A. Griffin Excitations in a Bose-condensed Liquid , 1993 .

[11]  William J. Trenberth Global well-posedness for the two-dimensional stochastic complex Ginzburg-Landau equation , 2019, 1911.09246.

[12]  B. Najman Time singular limit of semilinear wave equations with damping , 1993 .

[13]  Y. Inahama,et al.  Stochastic complex Ginzburg-Landau equation with space-time white noise , 2017, 1702.07062.

[14]  Oscillating superfluidity of bosons in optical lattices. , 2002, Physical review letters.

[15]  S. Albeverio,et al.  Trivial solutions for a non-lineartwo-space dimensional wave equation perturbed by space-time white noise , 1996 .

[16]  W. Schlag,et al.  Long time dynamics for damped Klein-Gordon equations , 2015, 1505.05981.

[17]  M. Gubinelli,et al.  Renormalization of the two-dimensional stochastic nonlinear wave equations , 2017, Transactions of the American Mathematical Society.

[18]  M. Hoshino Global well-posedness of complex Ginzburg–Landau equation with a space–time white noise , 2017, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques.

[19]  R. Danchin,et al.  Fourier Analysis and Nonlinear Partial Differential Equations , 2011 .

[20]  Takahisa Inui The Strichartz estimates for the damped wave equation and the behavior of solutions for the energy critical nonlinear equation , 2019, Nonlinear Differential Equations and Applications NoDEA.

[21]  M. Hoshino Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation , 2016, 1605.02624.

[22]  Tadahiro Oh,et al.  A remark on triviality for the two-dimensional stochastic nonlinear wave equation , 2019, Stochastic Processes and their Applications.

[23]  Kiyosi Itô Complex Multiple Wiener Integral , 1952 .

[24]  K. Nakanishi,et al.  Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation , 2003 .

[25]  Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces , 2019, 1904.06792.