Publications by Daniel Tataru | EPFL Graph Search

A lunar reconnaissance drone for cooperative exploration and high-resolution mapping of extreme locations

David Rodriguez Martinez, Daniel Tataru, Erik Uythoven, Thomas Pfeiffer

An efficient characterization of scientifically significant locations is essential prior to the return of humans to the Moon. The highest resolution imagery acquired from orbit of south-polar shadowed regions and other relevant locations remains, at best, ...

Pergamon-Elsevier Science Ltd2024

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Joachim Krieger, Daniel Tataru

We consider the hyperbolic Yang-Mills equation on the Minkowski space

\reels^{4+1}

. Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem. ...

Annal Mathematics2017

Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy

Joachim Krieger, Daniel Tataru

We prove that the critical Maxwell-Klein-Gordon equation on R4+1 is globally well-posed for smooth initial data which are small in the energy norm. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of ...

Duke Univ Press2015

A codimension two stable manifold of near soliton equivariant wave maps

Joachim Krieger, Daniel Tataru

We consider finite-energy equivariant solutions for the wave map problem from ℝ2+1 to S2 which are close to the soliton family. We prove asymptotic orbital stability for a codimension-two class of initial data which is small with respect to a stronger topo ...

Mathematical Science Publ2013

Renormalization and blow up for the critical Yang-Mills problem

Joachim Krieger, Daniel Tataru

We consider the Yangs-Mills equations in 4 + 1 dimensions. This is the energy critical case and we show that it admits a family of solutions which blow up in finite time. They are obtained by the spherically symmetric ansatz in the SO(4) gauge group and re ...

2009

Slow Blow-Up Solutions For The H-1(R-3) Critical Focusing Semilinear Wave Equation

Joachim Krieger, Daniel Tataru

Given v > 1/2 and 8 > 0 arbitrary, we prove the existence of energy solutions of ...

2009

Renormalization and blow up for charge one equivariant critical wave maps

Joachim Krieger, Daniel Tataru

We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+ 1 -> S-2 of the form u( t, r) = Q(lambda( t) r) + R(t, r) where u is the polar angle on the sphere, Q(r) = 2 arctan r is the ground state harmonic map, la ...

Springer Verlag2008

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A lunar reconnaissance drone for cooperative exploration and high-resolution mapping of extreme locations

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy

Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy

A codimension two stable manifold of near soliton equivariant wave maps

Renormalization and blow up for the critical Yang-Mills problem

Slow Blow-Up Solutions For The H-1(R-3) Critical Focusing Semilinear Wave Equation

Renormalization and blow up for charge one equivariant critical wave maps

Renormalization and blow up for the critical Yang-Mills problem

Slow Blow-Up Solutions For The H-1(R-3) Critical Focusing Semilinear Wave Equation

Global Well-Posedness For The Maxwell-Klein-Gordon Equation In 4+1 Dimensions: Small Energy

Renormalization and blow up for charge one equivariant critical wave maps

A codimension two stable manifold of near soliton equivariant wave maps

A lunar reconnaissance drone for cooperative exploration and high-resolution mapping of extreme locations

Global well-posedness for the Yang-Mills equation in 4+1 dimensions: Small energy