Si stabilisce la risolubilità di tre problemi ai valori iniziali e al contorno per il sistema ottenuto linearizzando le equazioni della MHD. Le equazioni contengono termini corrispondenti alle correnti di Hall e di ion-slip. Le soluzioni sono trovate negli spazi di Sobolev \( W_{p}^{2,1} (Q_{T} ) \) con \( p > 5/2 \) e negli spazi di Holder anisotropi.
Referenze Bibliografiche
[1]
S. I. PAI,
Magnetogasdynamics and Plasma Dynamics.
Springer-Verlag, New York
1962. |
MR 137449 |
Zbl 0122.44305[2]
J. A. SHERCLIFF,
A Textbook of Magnetohydrodynamics.
Pergamon, Oxford
1965. |
MR 185961[3] G. SUTTON - A. SHERMAN, Engineering Magnetohydrodynamics. McGraw-Hill, 1965.
[4]
M. MAIELLARO,
Uniqueness of M. H. D. thermodiffusive mixture flows with Hall and ion-slip effects.
Meccanica, vol.
12, 1,
1977, 9-14. |
Zbl 0401.76091[5]
S. RIONERO,
Sulla stabilità magnetofluidodinamica non lineare asintotica in media in presenza di effetto Hall.
Ricerche Mat., vol.
20, 2,
1971, 285-296. |
MR 343759 |
Zbl 0236.76043[6]
M. MAIELLARO -
L. PALESE,
Electrical anisotropic effects on thermal instability.
Int. J. Engng. Sci., vol.
22, 4,
1984, 411-418. |
Zbl 0534.76045[7]
D. EBEL -
M. C. SHEN,
On the linear stability of a toroidal plasma with resistivity, viscosity and Hall current.
J. Mat. Anal. Appl., vol.
125,
1987, 81-103. |
fulltext (doi) |
MR 891351 |
Zbl 0649.76023[8]
D. EBEL -
M. C. SHEN,
Linearization principle for a toroidal Hall current plasma with viscosity and resistivity.
Ann. Mat. Pura Appl., vol.
150,
1988, 39-65. |
fulltext (doi) |
MR 946029 |
Zbl 0666.76153[9]
G. MULONE -
F. SALEMI,
Some continuous dependence theorems in MHD with Hall and ion-slip currents in unbounded domains.
Rend. Accad. Sci. Fis. Mat. Napoli, s. IV, vol.
55,
1988, 139-152. |
MR 1136744 |
Zbl 1145.76473[10]
G. P. GALDI -
M. PADULA,
A new approach to energy theory in the stability of fluid motion.
Arch. Rational Mech. Anal., vol.
110,
1990, 187-286. |
fulltext (doi) |
MR 1060804 |
Zbl 0719.76035[11]
O. A. LADYZHENSKAYA -
V. A. SOLONNIKOV,
Solvability of evolution problems of magnetohydrodynamics.
Doklady Acad. Sci. USSR, vol.
124, 1,
1959, 26-28. |
Zbl 0091.19804[12]
O. A. LADYZHENSKAYA -
V. A. SOLONNIKOV,
Resolution of some evolution problems of magnetohydrodynamics for a viscous incompressible fluid.
Trudy Math. Inst. Steklov, vol.
59,
1960, 115-173. |
MR 170130[13]
O. A. LADYZHENSKAYA -
V. A. SOLONNIKOV,
On linearization principle and on invariant manifolds for problems of magnetohydrodynamics.
Zapiski Nauchn. Semin. LOMI, vol.
38,
1973, 46-93 (in Russian); English transl.,
J. Soviet Math., vol.
8,
1977, 384-422. |
MR 377310 |
Zbl 0404.35089[14]
B. CARBONARO,
On the linearization principle in magnetohydrodynamics.
Ricerche Mat., vol.
28,
1979, 426-437. |
MR 578596 |
Zbl 0437.76050[15]
L. STUPJALIS,
On solvability of an initial-boundary value problem of magnetohydrodynamics.
Zapiski Nauchn. Semin. LOMI, vol.
69,
1977, 219-239 (in Russian); English transl.,
J. Soviet Math., vol.
10, 1,
1978, 155-170. |
MR 499834 |
Zbl 0389.76063[17]
V. A. SOLONNIKOV,
Estimates of solutions of nonstationary Navier-Stokes equations.
Zapiski Nauchn. Semin. LOMI, vol.
38,
1973, 153-231 (in Russian); English transl.,
J. Soviet Math., vol.
8, 1,
1977, 467-529. |
MR 415097 |
Zbl 0404.35081[18]
V. A. SOLONNIKOV,
On \( L_{p} \)-estimates of solutions of elliptic and parabolic systems.
Trudy Math. Inst. Steklov, vol.
102,
1967 (in Russian); English transl.,
Proc. Steklov Inst. Math., vol.
102,
1976, 157-185. |
MR 228809 |
Zbl 0204.42101[19]
SH. SAKHAEV -
V. A. SOLONNIKOV,
Estimates of solutions of a boundary value problem of magnetohydrodynamics.
Trudy Math. Inst. Steklov, vol.
127,
1975, 76-92 (in Russian); English transl.,
Proc. Steklov Inst. Math., vol.
127,
1975, 87-108. |
Zbl 0366.76091[20]
A. G. KHACHATRYAN,
Overdetermined parabolic boundary value problems.
Zap. Naucn. Sem. Len. LOMI, vol.
69,
1977, 240-277 (in Russian); English transl.,
J. Soviet Math., vol.
10, n. 1,
1978, 171-193. |
MR 467012 |
Zbl 0388.35035[21]
G. GRUBB -
V. A. SOLONNIKOV,
Reduction of basic initial-boundary value problems for the Stokes equations to initial-boundary value problems for parabolic systems of pseudodifferential equations.
Zapiski Nauchn. Semin. LOMI, vol.
163,
1987, 34-48 (in Russian); English transl.,
J. Soviet Math., vol.
49,
1990, 1140-1147. |
fulltext EuDML |
fulltext (doi) |
MR 918940 |
Zbl 0696.35130[22]
G. GRUBB -
V. A. SOLONNIKOV,
Reduction of basic initial-boundary value problems for the Navier-Stokes equations to initial-boundary value problems for nonlinear parabolic systems of pseudodifferential equations.
Zapiski Nauchn. Semin. LOMI, vol.
171,
1989, 36-52 (in Russian); English transl.,
Copenh. Univ. Math. Dept. Report., Ser.
1989, n.
5. |
fulltext EuDML |
fulltext (doi) |
MR 1031983 |
Zbl 0717.35069[23]
G. GRUBB -
V. A. SOLONNIKOV,
Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudodifferential methods.
Math. Scandinavica, vol.
69, 2,
1991, 217-291. |
fulltext EuDML |
MR 1156428 |
Zbl 0766.35034[24]
M. VISHIK,
On strongly elliptic systems of differential equations.
Mat. Sbornik, vol.
29,
1951, 615-676 (in Russian). |
MR 49440 |
Zbl 0044.09503[25]
V. A. SOLONNIKOV,
On boundary value problems for linear parabolic systems of differential equations of general form.
Trudy Math. Inst. Steklov, vol.
83,
1965 (in Russian); English transl.,
Proc. Steklov Inst. Math., vol.
83,
1965, 1-184. |
MR 211083 |
Zbl 0164.12502[26]
I. SH. MOGILEVSIĬ,
Estimates of solutions of the general initial-boundary value problem for the linear time-dependent system on Navier-Stokes equations in a bounded domain.
Trudy Math. Inst. Steklov, vol.
159,
1983, 61-94 (in Russian); English transl.,
Proc. Steklov Inst. Math., vol.
159,
1983, 61-95. |
MR 720208 |
Zbl 0548.35096[27]
I. SH. MOGILEVSIĬ,
On a boundary value problem for the time-dependent Stokes system with general boundary conditions. English transl.,
Math. USSR Izvestija, vol.
28, 1,
1987, 37-66. |
Zbl 0615.35077
Con il contributo del Ministero per i Beni e le Attività Culturali