TY - JOUR

T1 - Regularity of the Solution of the Prandtl Equation

AU - Petrov, V. E.

AU - Suslina, T. A.

N1 - Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/9

Y1 - 2021/9

N2 - Abstract: Solvability and regularity of the solution of the Dirichlet problem for the Prandtl equation (Formula presented.) is studied. Here p(x) is a positive function on (-1, 1) such that (Formula presented.). We introduce the scale of spaces (Formula presented.) in terms of the special integral transformation on the interval (-1, 1). We obtain theorems about the existence and uniqueness of the solution in the classes (Formula presented.) with (Formula presented.). In particular, for s = 1 the result is as follows: if (Formula presented.), then (Formula presented.), where (Formula presented.).

AB - Abstract: Solvability and regularity of the solution of the Dirichlet problem for the Prandtl equation (Formula presented.) is studied. Here p(x) is a positive function on (-1, 1) such that (Formula presented.). We introduce the scale of spaces (Formula presented.) in terms of the special integral transformation on the interval (-1, 1). We obtain theorems about the existence and uniqueness of the solution in the classes (Formula presented.) with (Formula presented.). In particular, for s = 1 the result is as follows: if (Formula presented.), then (Formula presented.), where (Formula presented.).

KW - Fourier integral transformation

KW - integral transformation on the interval

KW - Prandtl equation

KW - weak solution

UR - http://www.scopus.com/inward/record.url?scp=85118174435&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/27ba0b86-146e-3f27-a894-35d3445e0578/

U2 - 10.1134/S0001434621090248

DO - 10.1134/S0001434621090248

M3 - Article

AN - SCOPUS:85118174435

VL - 110

SP - 543

EP - 559

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 3-4

ER -