@Article{CMAA-2-289,
author = {Dias , João Paulo and Frid , Hermano},
title = {On Short Wave-Long Wave Interactions in the Relativistic Context: Application to the Relativistic Euler Equations},
journal = {Communications in Mathematical Analysis and Applications},
year = {2023},
volume = {2},
number = {3},
pages = {289--303},
abstract = {<p style="text-align: justify;">In this paper we introduce a model of relativistic short wave-long
wave interaction where the short waves are described by the massless (1+3)-dimensional Thirring model of nonlinear Dirac equation and the long waves
are described by the (1+3)-dimensional relativistic Euler equations. The interaction coupling terms are modeled by a potential proportional to the relativistic
specific volume in the Dirac equation and an external force proportional to the
square modulus of the Dirac wave function in the relativistic Euler equation.
An important feature of the model is that the Dirac equations are based on the
Lagrangian coordinates of the relativistic fluid flow. In particular, an important
contribution of this paper is a clear formulation of the relativistic Lagrangian
transformation. As far as the authors know the definition of the Lagrangian
transformation given in this paper is new. Finally, we establish the short-time
existence and uniqueness of a smooth solution of the Cauchy problem for the
regularized model. This follows through the symmetrization of the relativistic
Euler equation introduced by Makino and Ukai (1995) and requires a slight extension of a well known theorem of T. Kato (1975) on quasi-linear symmetric
hyperbolic systems.</p>},
issn = {2790-1939},
doi = {https://doi.org/10.4208/cmaa.2023-0005},
url = {http://global-sci.org/intro/article_detail/cmaa/22015.html}
}