PERTURBATION THEOREMS FOR LINEAR HYPERBOLIC MIXED PROBLEMS AND APPLICATIONS TO THE COMPRESSIBLE EULER EQUATIONS

被引:31
作者
DAVEIGA, HB
机构
[1] Centro Linceo Interdisciplinare, Accademia Nazionale Dei Lincei
关键词
D O I
10.1002/cpa.3160460206
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main result of this paper (which is completely new, apart from our previous and less general result proved in reference [9]) states that the nonlinear system of equations (1.11) (or, equivalently, (1.10)) that describes the motion of an inviscid, compressible (barotropic) fluid in a bounded domain OMEGA, gives rise to a strongly well-posed problem (in the Hadamard classical sense) in spaces H(k)(OMEGA), k greater-than-or-equal-to 3; see Theorem 1.4 below. Roughly speaking, if (a(n), phi(n)) --> (a, phi) in H(k) x H(k) and if f(n) --> f in L2(0, T; H(k)), then (v(n), g(n)) --> (v, g) in C(0, T; H(k) x H(k)). The method followed here (see also [8]) also applies to the non-barotropic case p = p(p, s) (see [10]) and to other nonlinear problems. These results are based upon an improvement of the structural-stability theorem for linear hyperbolic equations. See Theorem 1.2 below. Added in proof. The reader is referred to [29], Part I, for a concise explanation of some fundamental points in the method followed here.
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页码:221 / 259
页数:39
相关论文
共 29 条
[1]  
Agemi R., 1981, HOKKAIDO MATH J, V10, P156
[2]  
[Anonymous], COMPRESSIBLE FLUID F
[3]  
Beirao Da Veiga H., 1988, REND SEMIN MAT U PAD, V97, P247
[4]  
Bourguinon J.P., 1975, J FUNCT ANAL, V15, P341
[5]   DATA DEPENDENCE IN THE MATHEMATICAL-THEORY OF COMPRESSIBLE INVISCID FLUIDS [J].
DAVEIGA, HB .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1992, 119 (02) :109-127
[6]  
DAVEIGA HB, 1980, ANN MAT PUR APPL, V125, P279, DOI DOI 10.1007/BF01789415
[7]  
DAVEIGA HB, 1979, CR HEBD ACAD SCI, V289, P297
[8]  
DAVEIGA HB, IN PRESS ANN MAT PUR
[9]  
DAVEIGA HB, 1991, IN PRESS J NONLINEAR
[10]  
DAVEIGA HB, 1981, ANN SC NORM SUP PISA, V8, P317