Global existence for solutions of □u = A¦u¦p
Global existence for solutions of □u = A¦u¦p
复制标题
□u = Aμuμp 解的全局存在性
DOI：
10.1016/0022-0396(89)90169-1
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发表时间：
1989
影响因子：
2.4
通讯作者：
Y. Choquet
中科院分区：
文献类型：
--
作者：
Y. Choquet
F. John [2]证明了在n= 3的情形下，当Cauchy数据u1 I= 0= cp，a，uI，=，，=@，cp，+ EQ（R”），C”函数在R”上具有紧支集时，方程在IR”x R上有整体解. Kato [3]和Sideris [6]将不存在部分推广到n> 3的情形，并给出了平均值为~ 5的条件，证明了当1< p< pa（n），PO（n）为正根时不存在解，如n= 3的情形，多项式（n-1）x2-（n+ 1）x-2。我们证明了当0被整体双曲流形（V，xR，g）的波算子V”a代替时，当V，紧且p> 1时，这种不存在性.
F. John [2] has proved in the case n= 3 that the equation has a global solution on IR” x R for small enough Cauchy data u 1 I= 0= cp, a, u I,=,,=@, cp,+ EQ (R”), C” functions on R” with compact support. The equation has no global solution with such Cauchy data-small or large-if 1< pc 1+ a and A~ 0.The nonexistence part as been extended to the case n> 3, with a condition of mean positiveness for~ 5, by Kato [3] and Sideris [6], which has proved the nonexistence for 1< p< pa (n), with PO (n) the positive root, as in the case n= 3, of the polynomial (n-1) x2-(n+ 1) x-2. We have proved [lo] this nonexistence when 0 is replaced by the wave operator V” a, of a globally hyperbolic manifold (V, x R, g) with V, compact and p> 1.