S. Albeverio, Z. Haba, and F. Russo, Trivial solutions for a nonlinear two-space-dimensional wave equation perturbed by space-time white noise, Stochastics, vol.56, issue.1-2, pp.127-160, 1996.

S. Albeverio, Z. Haba, and F. Russo, A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise, Probab. Theory Relat. Fields, vol.121, issue.3, pp.319-366, 2001.

N. Aronszajn and K. Smith, Theory of Bessel potentials, I. Ann. Inst. Fourier (Grenoble), vol.11, pp.385-475, 1961.

A. Barone, F. Esposito, C. Magee, and A. Scott, Theory and applications of the sine-Gordon equation, Rivista del Nuovo Cimento, vol.1, pp.227-267, 1971.

Á. Bényi and T. Oh, The Sobolev inequality on the torus revisited, Publ. Math. Debrecen, vol.83, issue.3, pp.359-374, 2013.

J. Bourgain, Periodic nonlinear Schrödinger equation and invariant measures, Commun. Math. Phys, vol.166, pp.1-26, 1994.

J. Bourgain, Invariant measures for the 2D-defocusing nonlinear Schrödinger equation, Commun. Math. Phys, vol.176, pp.421-445, 1996.

A. Chandra, M. Hairer, and H. Shen, The dynamical sine-Gordon model in the full subcritical regime

M. Christ and M. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal, vol.100, pp.87-109, 1991.

G. Da-prato and A. Debussche, Strong solutions to the stochastic quantization equations, Ann. Probab, vol.31, issue.4, pp.1900-1916, 2003.

G. Da-prato and J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications, vol.152, 2014.

E. W. Jentzen, A. Shen, and H. , Renormalized powers of Ornstein-Uhlenbeck processes and wellposedness of stochastic Ginzburg-Landau equations, Nonlinear Anal, vol.142, pp.152-193, 2016.

J. Fröhlich, Classical and quantum statistical mechanics in one and two dimensions: two-component Yukawa-and Coulomb systems, Commun. Math. Phys, vol.47, issue.3, pp.233-268, 1976.

C. Garban, Dynamical Liouville. J. Funct. Anal, vol.278, issue.6, p.108351, 2020.

A. E. Gatto, Product rule and chain rule estimates for fractional derivatives on spaces that satisfy the doubling condition, J. Funct. Anal, vol.188, issue.1, pp.27-37, 2002.

J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal, vol.133, pp.50-68, 1995.

L. Grafakos, Classical Fourier analysis, Graduate Texts in Mathematics, vol.249, p.638, 2014.

L. Grafakos, Modern Fourier analysis, Graduate Texts in Mathematics, vol.250, p.624, 2014.

M. Gubinelli, H. Koch, and T. Oh, Renormalization of the two-dimensional stochastic nonlinear wave equation, Trans. Am. Math. Soc, vol.370, pp.7335-7359, 2018.

M. Gubinelli, H. Koch, and T. Oh, Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity

M. Gubinelli, H. Koch, T. Oh, and L. Tolomeo, Global dynamics for the two-dimensional stochastic nonlinear wave equations

M. Hairer, A theory of regularity structures, Invent. Math, vol.198, pp.269-504, 2014.

M. Hairer, M. D. Ryser, and H. Weber, Triviality of the 2D stochastic Allen-Cahn equation, Electron. J. Probab, vol.17, issue.39, p.14, 2012.

M. Hairer and H. Shen, The dynamical sine-Gordon model, Commun. Math. Phys, vol.341, issue.3, pp.933-989, 2016.

T. Kato, On nonlinear Schrödinger equations. II. H s -solutions and unconditional well-posedness, J. Anal. Math, vol.67, pp.281-306, 1995.

M. Keel and T. Tao, Endpoint Strichartz estimates, Am. J. Math, vol.120, issue.5, pp.955-980, 1998.

R. Killip, B. Stovall, and M. Visan, Blowup behaviour for the nonlinear Klein-Gordon equation, Math. Ann, vol.358, pp.289-350, 2014.

H. Lacoin, R. Rhodes, and V. Vargas, Complex Gaussian multiplicative chaos, Commun. Math. Phys, vol.337, issue.2, pp.569-632, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00914380

H. Lacoin, R. Rhodes, and V. Vargas, A probabilistic approach of ultraviolet renormalisation in the boundary sine-Gordon model
URL : https://hal.archives-ouvertes.fr/hal-02114663

H. Lindblad and C. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal, vol.130, pp.357-426, 1995.

H. P. Mckean, The sine-Gordon and sinh-Gordon equations on the circle, Commun. Pure Appl. Math, vol.34, issue.2, pp.197-257, 1981.

H. P. Mckean and K. L. Vaninsky, Statistical mechanics of nonlinear wave equations, Trends and Perspectives in Applied Mathematics (Applied Mathematical Sciences, vol.100, pp.239-264, 1994.

T. Oh, M. Okamoto, and T. Robert, A remark on triviality for the two-dimensional stochastic nonlinear wave equation
URL : https://hal.archives-ouvertes.fr/hal-02434795

T. Oh, M. Okamoto, and N. Tzvetkov, Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation

T. Oh, O. Pocovnicu, and N. Tzvetkov, Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spaces

T. Oh, T. Robert, P. Sosoe, and Y. Wang, Invariant Gibbs dynamics for the dynamical sine-Gordon model

T. Oh, T. Robert, and N. Tzvetkov, Stochastic nonlinear wave dynamics on compact surfaces
URL : https://hal.archives-ouvertes.fr/hal-02434791

T. Oh, T. Robert, and Y. Wang, On the parabolic and hyperbolic Liouville equations
URL : https://hal.archives-ouvertes.fr/hal-02434800

T. Oh and L. Thomann, Invariant Gibbs measures for the 2-d defocusing nonlinear wave equations, Ann. Fac. Sci. Toulouse Math
URL : https://hal.archives-ouvertes.fr/hal-01498368

J. Perring and T. Skyrme, A model unified field equation, Nucl. Phys, vol.31, pp.550-555, 1962.

S. Ryang, T. Saito, and K. Shigemoto, Canonical stochastic quantization, Progr. Theoret. Phys, vol.73, issue.5, pp.1295-1298, 1985.

G. Staffilani, The initial value problem for some dispersive differential equations. Thesis (Ph.D.) -The University of, 1995.

C. Sun and N. Tzvetkov, New examples of probabilistic well-posedness for nonlinear wave equations, J. Funct. Anal, vol.278, issue.2, p.108322, 2020.

M. Taylor, Tools for PDE, pseudodifferential operators, paradifferential operators, and layer potentials, Mathematical Surveys and Monographs, vol.81, 2000.

, Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations