Regularity of the Solution of the Prandtl Equation

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Regularity of the Solution of the Prandtl Equation. / Petrov, V. E.; Suslina, T. A.

In: Mathematical Notes, Vol. 110, No. 3-4, 09.2021, p. 543-559.

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Petrov, V. E. ; Suslina, T. A. / Regularity of the Solution of the Prandtl Equation. In: Mathematical Notes. 2021 ; Vol. 110, No. 3-4. pp. 543-559.

BibTeX

@article{06b8a1a8a56041109b289567d96c6153,

title = "Regularity of the Solution of the Prandtl Equation",

abstract = "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.).",

keywords = "Fourier integral transformation, integral transformation on the interval, Prandtl equation, weak solution",

author = "Petrov, {V. E.} and Suslina, {T. A.}",

note = "Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = sep,

doi = "10.1134/S0001434621090248",

language = "English",

volume = "110",

pages = "543--559",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "3-4",

}

RIS

TY - JOUR

T1 - Regularity of the Solution of the Prandtl Equation

AU - Petrov, V. E.

AU - Suslina, T. A.

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 -

ID: 89595817