期刊
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
卷 8, 期 3, 页码 415-436出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219891611002457
关键词
Magnetohydrodynamics; zero magnetic diffusivity; strong solutions; existence and uniqueness
资金
- NSAF of China (China Scholarship Council)
- National Science Foundation [DMS-0906160]
- Office of Naval Research [N00014-07-1-0668]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0906160] Funding Source: National Science Foundation
The three-dimensional compressible magnetohydrodynamic isentropic flow with zero magnetic diffusivity is studied in this paper. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local-in-time strong solutions with large initial data is established. Strong solutions have weaker regularity than classical solutions. A generalized Lax-Milgram theorem and a Schauder-Tychonoff-type fixed-point argument are applied on conjunction with novel techniques and estimates for strong solutions.
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