In this review article we discuss a number of recent results concerning wild weak solutions of
the incompressible Euler and Navier–Stokes equations. These results build on the …

Lars Onsager, a giant of twentieth-century science and the 1968 Nobel Laureate in
Chemistry, made deep contributions to several areas of physics and chemistry. Perhaps less …

For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least
one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this …

Abstract For any α\lt1/3, we construct weak solutions to the 3D incompressible Euler
equations in the class C_tC_x^α that have nonempty, compact support in time on R*T^3 and …

We prove that given any $\beta< 1/3$, a time interval $[0, T] $, and given any smooth energy
profile $ e\colon [0, T]\to (0,\infty) $, there exists a weak solution $ v $ of the three …

This textbook presents a modern account of turbulence, one of the greatest challenges in
physics. The state-of-the-art is put into historical perspective five centuries after the first …

This series of books forms a unique and rigorous treatise on various mathematical aspects
of fluid mechanics models. These models consist of systems of nonlinear partial differential …

We propose a new point of view on weak solutions of the Euler equations, describing the
motion of an ideal incompressible fluid in \BbbR^n with n≥ 2. We give a reformulation of the …

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SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Inventiones …

We study the local equation of energy for weak solutions of three-dimensional
incompressible Navier-Stokes and Euler equations. We define a dissipation term D (u) …