Optimal convergence rates for the strong solutions to the compressible Navier–Stokes equations with potential force

2017 ◽  
Vol 34 ◽  
pp. 363-378 ◽  
Author(s):  
Wenjun Wang
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Potential Force ◽  
Navier Stokes Equations ◽  
Optimal Convergence ◽  
Optimal Convergence Rates

OPTIMAL CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH POTENTIAL FORCES

2007 ◽  
Vol 17 (05) ◽  
pp. 737-758 ◽  
Author(s):  
RENJUN DUAN ◽  
SEIJI UKAI ◽  
TONG YANG ◽  
HUIJIANG ZHAO
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Initial Perturbation ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Potential Force ◽  
Navier Stokes Equations ◽  
Optimal Convergence ◽  
Whole Space ◽  
Optimal Convergence Rates

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 Lp - 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.

scholarly journals Local Existence of Strong Solutions of a Fluid–Structure Interaction Model

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Sourav Mitra
Keyword(s):  
Stokes Equations ◽  
Local Existence ◽  
Interaction Model ◽  
Strong Solutions ◽  
Coupled System ◽  
Elastic Structure ◽  
Navier Stokes ◽  
Beam Equation ◽  
Navier Stokes Equations ◽  
System Coupling

AbstractWe are interested in studying a system coupling the compressible Navier–Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler–Bernoulli damped beam equation. We prove the local in time existence of strong solutions for that coupled system.

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