Well-posedness and critical thresholds in a nonlocal Euler system with relaxation. (English) Zbl 1486.35334
Summary: We propose and study a nonlocal Euler system with relaxation, which tends to a strictly hyperbolic system under the hyperbolic scaling limit. An independent proof of the local existence and uniqueness of this system is presented in any spatial dimension. We further derive a precise critical threshold for this system in one dimensional setting. Our result reveals that such nonlocal system admits global smooth solutions for a large class of initial data. Thus, the nonlocal velocity regularizes the generic finite-time breakdown in the pressureless Euler system.
MSC:
| 35Q31 | Euler equations |
| 35L65 | Hyperbolic conservation laws |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 76B03 | Existence, uniqueness, and regularity theory for incompressible inviscid fluids |
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