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

Revista Matemática Iberoamericana (1986)

- Volume: 2, Issue: 1-2, page 73-88
- ISSN: 0213-2230

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topKato, 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 > 1 + 2/p, 1 < p < ∞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 > 1 + 2/p, 1 < p < ∞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 -

## Citations in EuDML Documents

top- Ben Schweizer, On the three-dimensional Euler equations with a free boundary subject to surface tension
- Raphaël Danchin, Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque
- Misha Vishik, Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type

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