Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces

Commutator estimates and the euler and navier‐stokes equations

Tosio Kato, Gustavo Ponce · Communications on Pure and Applied Mathematics · 1988 · 1.8K citations

Global Analysis, Navier-stokes Equations, Commutator Estimates

Remarks on the breakdown of smooth solutions for the 3-D Euler equations

J. Thomas Beale, T. Kato, Andrew J. Majda · Communications in Mathematical Physics · 1984 · 1.5K citations

3-D Euler Equations, Global Analysis, Nonlinear Hyperbolic Problem +2

Groups of Diffeomorphisms and the Motion of an Incompressible Fluid

David G. Ebin, Jerrold E. Marsden · Annals of Mathematics · 1970 · 1.2K citations

Manifold Structure, Lie Group, Compressible Flow +11

The Cauchy problem for quasi-linear symmetric hyperbolic systems

Tosio Kato · Archive for Rational Mechanics and Analysis · 1975 · 897 citations

Cauchy Problem, Nonlinear Hyperbolic Problem, Hyperbolic Equation +1

Nonstationary flows of viscous and ideal fluids in R3

Tosio Kato · Journal of Functional Analysis · 1972 · 575 citations

Fluid Mechanics, Nonstationary Flows, Hydrodynamic Stability