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Bilinear virial identities and applications
We prove bilinear virial identities for the nonlinear Schrodinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear improvements to
Global existence for energy critical waves in 3-d domains
We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on for any smooth (compact) domain . The main ingredient in the proof is an spectral
Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay
We prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the
On well-posedness for the Benjamin–Ono equation
We prove existence and uniqueness of solutions for the Benjamin–Ono equation with data in $$H^{s}({\mathbb{R}})$$ , s > 1/4. Moreover, the flow is hölder continuous in weaker topologies.
An Extension of the Beale-Kato-Majda Criterion for the Euler Equations
Abstract: The Beale-Kato-Majda criterion asserts that smooth solutions to the Euler equations remain bounded past T as long as is finite, ohgr; being the vorticity. We show how to replace this by a
On Global Infinite Energy Solutions¶to the Navier-Stokes Equations¶in Two Dimensions
Abstract This paper studies the bidimensional Navier–Stokes equations with large initial data in the homogeneous Besov space . As long as r,q < +∞, global existence and uniqueness of solutions are
Self-similar solutions for navier-stokes equations in
We construct self-similar solutions for three-dimensional incompressible Navier-Stokes equations, providing some examples of functional spaces where this can be done. We apply our results to a
Blow-up of Critical Besov Norms at a Potential Navier–Stokes Singularity
We prove that if an initial datum to the incompressible Navier–Stokes equations in any critical Besov space $${\dot B^{-1+\frac 3p}_{p,q}({\mathbb {R}}^{3})}$$B˙p,q-1+3p(R3), with $${3 < p, q <