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Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. II. (English. Russian original) Zbl 0866.76096

Sib. Math. J. 35, No. 2, 250-259 (1994); translation from Sib. Mat. Zh. 35, No. 2, 278-287 (1994).
In the present article, which is a natural continuation of [the authors, Sib. Math. J. 35, No. 1, 9-20 (1994; Zbl 0840.76092); translation from Sib. Mat. Zh. 35, No. 1, 12-23 (1994)], we study well-posedness of mixed problems of stability of rotational discontinuity in magnetohydrodynamics with anisotropic pressure. Earlier we constructed an Hadamard-type example of ill-posedness for the linear mixed problem of stability of rotational discontinuity in the ordinary magnetohydrodynamics under the influence of a strong magnetic field. We construct the analogous example in the present article; namely, we construct an example of ill-posedness for the linear mixed problem of stability of rotational discontinuity in anisotropic magnetohydrodynamics (the Chu-Goldberg-Low model in the case of a cold plasma); i.e., we prove that in this case the rotational discontinuity is unstable.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory

Citations:

Zbl 0840.76092
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References:

[1] A. M. Blokhin and Yu. L. Trakhinin, ”Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. I,” Sibirsk. Mat. Zh.,35, No. 1, 12–24 (1994). · Zbl 0840.76092
[2] A. M. Blokhin and Yu. L. Trakhinin, ”Rotational discontinuity in magnetohydrodynamics,” Sibirsk. Mat. Zh.,34, No. 3, 3–18 (1993). · Zbl 0816.76093
[3] A. M. Blokhin and D. A. Krymskikh, ”Symmetrization of equations in magnetohydrodynamics with anisotropic pressure,” in: Boundary Value Problems for Partial Differential Equations [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk, 1990, pp. 3–19.
[4] A. M. Blokhin and I. Yu. Druzhinin, ”Well-posedness of some linear problems on stability of strong discontinuities in magnetohydrodynamics,” Sibirsk. Mat. Zh.,31, No. 2, 3–8 (1990). · Zbl 0712.76096
[5] S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979). · Zbl 0447.22011
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