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Article Dans Une Revue Nonlinearity Année : 2023

Instabilities Appearing in Effective Field theories: When and How?

Jean-Pierre Eckmann
  • Fonction : Auteur
Farbod Hassani
  • Fonction : Auteur
Hatem Zaag

Résumé

Nonlinear partial differential equations appear in many domains of physics, and we study here a typical equation which one finds in effective field theories (EFT) originated from cosmological studies. In particular, we are interested in the equation $\partial_t^2 u(x,t) = \alpha (\partial_x u(x,t))^2 +\beta \partial_x^2 u(x,t)$ in $1+1$ dimensions. It has been known for quite some time that solutions to this equation diverge in finite time, when $\alpha >0$. We study the detailed nature of this divergence as a function of the parameters $\alpha>0 $ and $\beta\ge0$. The divergence does not disappear even when $\beta $ is very large contrary to what one might believe. But it will take longer to appear as $\beta$ increases when $\alpha$ is fixed. We note that there are two types of divergence and we discuss the transition between these two as a function of parameter choices. The blowup is unavoidable unless the corresponding equations are modified. Our results extend to $3+1$ dimensions.

Dates et versions

hal-03873076 , version 1 (26-11-2022)

Identifiants

Citer

Jean-Pierre Eckmann, Farbod Hassani, Hatem Zaag. Instabilities Appearing in Effective Field theories: When and How?. Nonlinearity, 2023, 36 (9), pp.4844-4861. ⟨10.1088/1361-6544/ace769⟩. ⟨hal-03873076⟩
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