论文标题
prandtl方程溶液的规律性
Regularity of the solution of the Prandtl equation
论文作者
论文摘要
prandtl方程的dirichlet问题解决方案的解决性和规律性$$ {u（x）\ p（x）} - {1 \ over2π} \ foce t-int _ { - 1}^1}^1 {u'（t）\ t-x} \ contert t-x} \ contert t-x} \，dt = f（x）$ $。假定$ p（x）$是$（-1,1）$的正函数，因此$ \ sup \ frac {（1-x^2）} {p（x）} <\ infty $。我们在间隔$（-1,1）$上的特殊积分转换方面介绍了空间$ \ widetilde {h}^s（-1,1）$。我们在类中获得有关解决方案的存在和独特性的定理，$ \ widetilde {h}^{s}（ - 1,1）$，$ 0 \ le s \ le s \ le 1 $。特别是，对于$ s = 1 $，结果如下：如果$ r^{1/2} f \在l_2 $中，然后$ r^{ - 1/2} u，r^{1/2} u'\ in L_2 $，其中$ r（x）= 1-x^2 $。
Solvability and regularity of the solution of the Dirichlet problem for the Prandtl equation $$ {u(x)\over p(x)}- {1\over 2π}\int_{-1}^1 {u'(t) \over t-x} \,dt = f(x) $$ is studied. It is assumed that $p(x)$ is a positive function on $(-1,1)$ such that $\sup \frac{(1-x^2)}{ p(x)} < \infty$. We introduce the scale of spaces $\widetilde{H}^s(-1,1)$ in terms of the special integral transformation on the interval $(-1,1)$. We obtain theorem about existence and uniqueness of the solution in the classes $\widetilde{H}^{s}(-1,1)$ with $0\le s \le 1$. In particular, for $s=1$ the result is as follows: if $r^{1/2} f \in L_2$, then $r^{-1/2} u, r^{1/2} u' \in L_2$, where $r(x)=1-x^2$.
