Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).

Kato, Tosio, and Ponce, Gustavo. "Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).." Revista Matemática Iberoamericana 2.1-2 (1986): 73-88. <http://eudml.org/doc/39302>.

@article{Kato1986,
abstract = {In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s &gt; 1 + 2/p, 1 &lt; p &lt; ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.},
author = {Kato, Tosio, Ponce, Gustavo},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios LP; Corriente de fluidos; pseudo-differential operator; Banach algebra; Volterra integral equation; evolution operator; vorticity equation; equicontinuity; diffeomorphism; well-posedness; existence; uniqueness; persistence; fluid dynamical equations; Navier-Stokes; Euler equations; incompressible fluids; Lebesgue spaces},
language = {eng},
number = {1-2},
pages = {73-88},
title = {Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).},
url = {http://eudml.org/doc/39302},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Kato, Tosio
AU - Ponce, Gustavo
TI - Well-posedness of the Euler and Navier-Stokes equations in the Lebesque spaces Lsp(R2).
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 1-2
SP - 73
EP - 88
AB - In this paper we show that the Euler equation for incompressible fluids in R2 is well posed in the (vector-valued) Lebesgue spacesLsp = (1 - ∆)-s/2 Lp(R2) with s &gt; 1 + 2/p, 1 &lt; p &lt; ∞and that the same is true of the Navier-Stokes equation uniformly in the viscosity ν.
LA - eng
KW - Espacios LP; Corriente de fluidos; pseudo-differential operator; Banach algebra; Volterra integral equation; evolution operator; vorticity equation; equicontinuity; diffeomorphism; well-posedness; existence; uniqueness; persistence; fluid dynamical equations; Navier-Stokes; Euler equations; incompressible fluids; Lebesgue spaces
UR - http://eudml.org/doc/39302
ER -