Shock Waves In Conservation Laws With Physical Viscosity (memoirs Of The American Mathematical Society)
by Tai-Ping Liu /
2015 / English / PDF
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The authors study the perturbation of a shock wave in conservation
laws with physical viscosity. They obtain the detailed pointwise
estimates of the solutions. In particular, they show that the
solution converges to a translated shock profile. The strength of
the perturbation and that of the shock are assumed to be small but
independent. The authors' assumptions on the viscosity matrix are
general so that their results apply to the Navier-Stokes equations
for the compressible fluid and the full system of
magnetohydrodynamics, including the cases of multiple eigenvalues
in the transversal fields, as long as the shock is classical. The
authors' analysis depends on accurate construction of an
approximate Green's function. The form of the ansatz for the
perturbation is carefully constructed and is sufficiently tight so
that the author can close the nonlinear term through Duhamel's
principle.
The authors study the perturbation of a shock wave in conservation
laws with physical viscosity. They obtain the detailed pointwise
estimates of the solutions. In particular, they show that the
solution converges to a translated shock profile. The strength of
the perturbation and that of the shock are assumed to be small but
independent. The authors' assumptions on the viscosity matrix are
general so that their results apply to the Navier-Stokes equations
for the compressible fluid and the full system of
magnetohydrodynamics, including the cases of multiple eigenvalues
in the transversal fields, as long as the shock is classical. The
authors' analysis depends on accurate construction of an
approximate Green's function. The form of the ansatz for the
perturbation is carefully constructed and is sufficiently tight so
that the author can close the nonlinear term through Duhamel's
principle.
