Convolution of radius functions on ℝ³

• Autorzy: Konstanty Holly
• Języki publikacji: EN

Abstrakty

EN

We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in the boundary layer.

Słowa kluczowe

EN

integral formulas; asymptotic behaviour of convolution at ∞

Kategorie tematyczne

• 26B20: Integral formulas (Stokes, Gauss, Green, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 1
• Strony: 1-32

Daty

wydano

1994

otrzymano

1989-06-06

poprawiono

1990-10-15

poprawiono

1993-11-25

Twórcy

autor

Konstanty Holly

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] K. Holly, Navier-Stokes equations in ℝ³ as a system of nonsingular integral equations of Hammerstein type. An abstract approach, Univ. Iagel. Acta Math. 28 (1991), 151-161.
• [2] K. Holly, Navier-Stokes equations in ℝ³: relations between pressure and velocity, Internat. Conf. 'Nonlinear Differential Equations', Varna 1987, unpublished.
• [3] N. S. Landkof, Foundations of Modern Potential Theory, Nauka, Moscow, 1966 (in Russian).
• [4] M. Riesz, Intégrales de Riemann-Liouville et potentiels, Acta Sci. Math. (Szeged) 9 (1938), 1-42.