一类半线性波动方程的低正则性估计

Minimal Regularity Estimates for a Class of Semilinear Wave Equations

对形如utt-△u=uk(Du) α(x∈R3 ,k∈Z+ ,l =｜α｜=2 )的半线性波动方程在三维空间中的Sobolev指数进行了研究 ,用较简单的方法得到了与KlainermanS.和MachedomM .(ArchRatMechAnal,1992 ,86 (5 ) :36 9)相同的结果 ,即Sobolev指数为 2 .

The Sobolev exponent in three space di mensions of semilinear wave equations of the form u tt -△u=u k(Du) α, (x∈R 3, k∈Z +, l=｜α｜=2), is investigated. The m ethod used here is simpler than that of Klainerman and Machedom (Arch Rat Mech A nal,1992,86(5):369), but the same result that the exponent 2 is resumed.