Vanishing magnetic field limits of solutions to the pressureless magnetogasdynamics. (English) Zbl 1403.35231
Summary: We are interested in the system of conservation laws modeling the pressureless magnetogasdynamics. Firstly, we solve the Riemann problem and obtain five kinds of structures consisting of combinations of shocks, rarefaction waves and contact discontinuities. Secondly, we study the vanishing magnetic field limits of the Riemann solutions to the pressureless magnetogasdynamics and show that the density and velocity in the Riemann solutions to the pressureless magnetogasdynamics converge to the Riemann solutions to the pressureless gas dynamics. The formation processes of delta-shocks and vacuum states are discussed in details.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35L65 | Hyperbolic conservation laws |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35B25 | Singular perturbations in context of PDEs |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76N15 | Gas dynamics (general theory) |
| 76L05 | Shock waves and blast waves in fluid mechanics |
Keywords:
pressureless magnetogasdynamics; pressureless gas dynamics; vanishing magnetic field limits; delta-shocks; vacuum statesReferences:
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