TY - JOUR
T1 - Hydrodynamic limits of the nonlinear Klein-Gordon equation
AU - Lin, Chi Kun
AU - Wu, Kung Chien
N1 - Funding Information:
C.K. Lin is supported by National Science Council of Taiwan under the grant NSC98-2115-M-009-004-MY3. K.C. Wu is supported by the Tsz-Tza Foundation in Institute of Mathematics, Academia Sinica, Taipei, Taiwan. K.C. Wu would like to thank Dr. Clément Mouhot for his kind invitation to visit Cambridge during 2011–2012 academic year.
PY - 2012/9
Y1 - 2012/9
N2 - We perform the mathematical derivation of the compressible and incompressible Euler equations from the modulated nonlinear Klein-Gordon equation. Before the formation of singularities in the limit system, the nonrelativistic-semiclassical limit is shown to be the compressible Euler equations. If we further rescale the time variable, then in the semiclassical limit (the light speed kept fixed), the incompressible Euler equations are recovered. The proof involves the modulated energy introduced by Brenier (2000) [1].
AB - We perform the mathematical derivation of the compressible and incompressible Euler equations from the modulated nonlinear Klein-Gordon equation. Before the formation of singularities in the limit system, the nonrelativistic-semiclassical limit is shown to be the compressible Euler equations. If we further rescale the time variable, then in the semiclassical limit (the light speed kept fixed), the incompressible Euler equations are recovered. The proof involves the modulated energy introduced by Brenier (2000) [1].
UR - http://www.scopus.com/inward/record.url?scp=84865349883&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84865349883&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2012.02.002
DO - 10.1016/j.matpur.2012.02.002
M3 - Article
AN - SCOPUS:84865349883
SN - 0021-7824
VL - 98
SP - 328
EP - 345
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
IS - 3
ER -