Global solutions of the one-dimensional compressible Euler equations with nonlocal interactions via the inviscid limit
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic confinement. Both the polytropic gas law and the general gas law a...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Springer Nature
2025
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| Summary: | We are concerned with the global existence of finite-energy entropy solutions
of the one-dimensional compressible Euler equations with (possibly) damping,
alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic
confinement. Both the polytropic gas law and the general gas law are analyzed.
This is achieved by constructing a sequence of solutions of the one-dimensional
compressible Navier-Stokes-type equations with density-dependent viscosity
under the stress-free boundary condition and then taking the vanishing
viscosity limit. The main difficulties in this paper arise from the appearance
of the nonlocal terms. In particular, some uniform higher moment estimates for
the compressible Navier-Stokes equations on expanding intervals with
stress-free boundary conditions are obtained by careful design of the
approximate initial data. |
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