TY - JOUR
T1 - Optimal convergence rates for the compressible Navier-Stokes equations with potential forces
AU - Duan, Renjun
AU - Ukai, Seiji
AU - Yang, Tong
AU - Zhao, Huijiang
PY - 2007/5
Y1 - 2007/5
N2 - For the viscous and heat-conductive fluids governed by the compressible Navier-Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the L p - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded. © World Scientific Publishing Company.
AB - For the viscous and heat-conductive fluids governed by the compressible Navier-Stokes equations with an external potential force, there exist non-trivial stationary solutions with zero velocity. By combining the L p - Lq estimates for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the stationary profile in the whole space when the initial perturbation of the stationary solution and the potential force are small in some Sobolev norms. More precisely, the optimal convergence rates of the solution and its first order derivatives in L2-norm are obtained when the L1-norm of the perturbation is bounded. © World Scientific Publishing Company.
KW - Energy estimates
KW - Navier-Stokes equations
KW - Optimal convergence rate
UR - http://www.scopus.com/inward/record.url?scp=34248393109&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-34248393109&origin=recordpage
U2 - 10.1142/S021820250700208X
DO - 10.1142/S021820250700208X
M3 - RGC 21 - Publication in refereed journal
VL - 17
SP - 737
EP - 758
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 5
ER -