arXiv subjects

Jacek Jendrej

Publications and source records attributed to Jacek Jendrej.

39 records · Page 3Linked to original sources

arXiv2015

Nonexistence of radial two-bubbles with opposite signs for the energy-critical wave equation

We consider the focusing energy-critical wave equation in space dimension $N \geq 3$ for radial data. We study two-bubble solutions, that is solutions which behave as a superposition of two decoupled radial ground states (called bubbles) asymptotically for large positive times. We prove that in this case these two bubbles must have the same sign. The main tool is a sharp coercivity property of the energy functional near the family of ground states.

math.AP↗

arXiv2015

Bounds on the speed of type II blow-up for the energy critical wave equation in the radial case

We consider the focusing energy-critical wave equation in space dimension $N\in \{3, 4, 5\}$ for radial data. We study type II blow-up solutions which concentrate one bubble of energy. It is known that such solutions decompose in the energy space as a sum of the bubble and an asymptotic profile. We prove bounds on the blow-up speed in the case when the asymptotic profile is sufficiently regular. These bounds are optimal in dimension $N = 5$. We also prove that if the asymptotic profile is sufficiently regular, then it cannot be strictly negative at the origin.

math.AP↗

arXiv2013

Small time heat kernel asymptotics at the cut locus on surfaces of revolution

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate point and present the consequences of this result to the small time heat kernel asymptotics at this point. These results give a first example where the minimal degeneration of the asymptotic expansion at the cut locus is attained.

math.AP↗