Jacek Jendrej

activity

20122026

most citedConstruction of type II blow-up solutions for the energy-critical wave equation in dimension 5

57 citations · 196 across the 37 of their papers we have counts for

collaborators

39 papers

math.NT2026

Quantitative lower bound for Pythagorean pairs in boxes of prime powers

Rongzhong Xiao

For each positive integer $N$ , let $p_{i}$ be the $i$ -th prime for $i \in {1, \dots, N}$ , and set $Φ_{N} = {i = 1 \prod N p_{i}^{a_{i}} : a_{i} \in {0, 1, \dots, N - 1}} .$ Write $f(…

math.AP2026

Construction of two-bubble solutions for the energy-critical NLS in dimension 6

Jacek Jendrej, Xuemei Li, Guixiang Xu

We construct pure two-bubble solutions for the energy-critical focusing nonlinear Schrödinger equation in space dimension $N = 6$ . They are global in (at least) one time direction…

math.AP2026

Nonexistence of blow-up solutions with smooth radiation for energy-critical equivariant wave maps

Jacek Jendrej, Yuchen Yin, Lifeng Zhao

We study $k$ -equivariant energy critical wave maps $R^{1 + 2} \to S^{2}$ , for any equivariance degree $k \geq 2$ . We prove that the radiation associated with any finite…

math.AP2026

Construction of multi-bubble solutions for the energy-critical wave equation in dimension four

Jingyuan Gu, Jacek Jendrej, Lifeng Zhao

For any $N \geq 2$ , we construct a global solution of the energy-critical focusing wave equation in dimension four which blows up in infinite time at $N$ prescribed points $z_1,\ldo…

math.AP2026

Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five

Jacek Jendrej, Chencheng Zhang, Lifeng Zhao

We study the asymptotic dynamics of multi-bubble solutions to the focusing energy-critical wave equation in five dimensions. Assuming that the solution asymptotically decomposes in…

math.AP2026

High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation

Jacek Jendrej, Tony Salvi

We investigate the global well-posedness and modified scattering for the one-dimensional Schrödinger equation with gauge-invariant polynomial nonlinearity. For small localized init…

math.AP2026

Construction of two-bubble solutions for the energy-critical Hartree equation

Jacek Jendrej, Xuemei Li, Guixiang Xu

We construct a pure two-bubble solution for the focusing, energy-critical Hartree equation in space dimension $N \geq 7$ . The constructed solution is spherically symmetric, global…

math.AP2025

Rate of convergence to equilibrium for the heated string

Tomasz Cieślak, Jacek Jendrej, Christian Stinner

In the present manuscript, we calculate the exponential rate of convergence of the heated string system (a mixed-type hyperbolic-parabolic system of PDEs) towards the equilibrium,…

math.AP2025

Concentric bubbles concentrating in finite time for the energy critical wave maps equation

Jacek Jendrej, Joachim Krieger

We show that the energy critical Wave Maps equation from $R^{2 + 1}$ to $S^{2}$ and restricted to the co-rotational setting with co-rotation index $k = 2$ admits fini…

math.AP2025

Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation

Asma Azaiez, Jacek Jendrej, Hatem Zaag

This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show…

math.AP2024

Classification of kink clusters for scalar fields in dimension 1+1

Jacek Jendrej, Andrew Lawrie

We consider a real scalar field equation in dimension 1+1 with an even, positive self-interaction potential having two non-degenerate zeros (vacua) 1 and -1. Such a model admits no…

math.AP2024

Multisoliton solutions for equivariant wave maps on a $2 + 1$ dimensional wormhole

Piotr Bizoń, Jacek Jendrej, Maciej Maliborski

We study equivariant wave maps from the $2 + 1$ dimensional wormhole to the 2-sphere. This model has explicit harmonic map solutions which, in suitable coordinates, have the form of…

math.AP2024

Wave maps in dimension $1 + 1$ with an external forcing

Zdzisław Brzeźniak, Jacek Jendrej, Nimit Rana

This paper aims to establish the local and global well-posedness theory in $L^{1}$ , inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave…

math.AP2023★ 1 cited

Continuous in time bubble decomposition for the harmonic map heat flow

Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag

We consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen seque…

math.AP2023★ 1 cited

Dynamics of kink clusters for scalar fields in dimension 1+1

Jacek Jendrej, Andrew Lawrie

We consider a real scalar field equation in dimension 1+1 with an even positive self-interaction potential having two non-degenerate zeros (vacua) 1 and -1. It is known that such a…

math.AP2023

Asymptotic stability and classification of multi-solitons for Klein-Gordon equations

Gong Chen, Jacek Jendrej

Focusing on multi-solitons for the Klein-Gordon equations, in first part of this paper, we establish their conditional asymptotic stability. In the second part of this paper, we cl…

math.AP2022

Bubble decomposition for the harmonic map heat flow in the equivariant case

Jacek Jendrej, Andrew Lawrie

We consider the harmonic map heat flow for maps from the plane taking values in the sphere, under equivariant symmetry. It is known that solutions to the initial value problem can…

math.AP2022★ 1 cited

Strichartz estimates for Klein-Gordon equations with moving potentials

Gong Chen, Jacek Jendrej

We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local…

math.AP2022

Statistical mechanics of the wave maps equation in dimension 1+1

Zdzisław Brzeźniak, Jacek Jendrej

We study wave maps with values in S^d, defined on the future light cone {|x| <= t}, with prescribed data at the boundary {|x| = t}. Based on the work of Keel and Tao, we prove that…

math.AP2022

Soliton resolution for the energy-critical nonlinear wave equation in the radial case

Jacek Jendrej, Andrew Lawrie

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $D \geq 4$ . This equation has a unique (up to sign and scale…

math.AP2021★ 3 cited

Kink networks for scalar fields in dimension 1+1

Gong Chen, Jacek Jendrej

We consider a scalar field equation in dimension $1 + 1$ with a positive external potential having non-degenerate isolated zeros. We construct weakly interacting pure multi-solitons,…

math.AP2021★ 2 cited

Nondegeneracy of heteroclinic orbits for a class of potentials on the plane

Jacek Jendrej, Panayotis Smyrnelis

In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the…

math.AP2021★ 1 cited

Soliton resolution for energy-critical wave maps in the equivariant case

Jacek Jendrej, Andrew Lawrie

We consider the equivariant wave maps equation $R^{1 + 2} \to S^{2}$ , in all equivariance classes $k \in N$ . We prove that every finite energy solution resol…

math.AP2020★ 2 cited

Continuous time soliton resolution for two-bubble equivariant wave maps

Jacek Jendrej, Andrew Lawrie

We consider the energy-critical wave maps equation from 1+2 dimensional Minkowski space into the 2-sphere, in the equivariant case. We prove that if a wave map decomposes, along a…

Quantitative lower bound for Pythagorean pairs in boxes of prime powers

Construction of two-bubble solutions for the energy-critical NLS in dimension 6

Nonexistence of blow-up solutions with smooth radiation for energy-critical equivariant wave maps

Construction of multi-bubble solutions for the energy-critical wave equation in dimension four

Rigidity of the multi-bubble solutions to the energy critical wave equation in dimension five

High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation

Construction of two-bubble solutions for the energy-critical Hartree equation

Rate of convergence to equilibrium for the heated string

Concentric bubbles concentrating in finite time for the energy critical wave maps equation

Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation

Classification of kink clusters for scalar fields in dimension 1+1

Multisoliton solutions for equivariant wave maps on a 2+1 dimensional wormhole

Wave maps in dimension 1+1 with an external forcing

Continuous in time bubble decomposition for the harmonic map heat flow

Dynamics of kink clusters for scalar fields in dimension 1+1

Asymptotic stability and classification of multi-solitons for Klein-Gordon equations

Bubble decomposition for the harmonic map heat flow in the equivariant case

Strichartz estimates for Klein-Gordon equations with moving potentials

Statistical mechanics of the wave maps equation in dimension 1+1

Soliton resolution for the energy-critical nonlinear wave equation in the radial case

Kink networks for scalar fields in dimension 1+1

Nondegeneracy of heteroclinic orbits for a class of potentials on the plane

Soliton resolution for energy-critical wave maps in the equivariant case

Continuous time soliton resolution for two-bubble equivariant wave maps

Multisoliton solutions for equivariant wave maps on a $2 + 1$ dimensional wormhole

Wave maps in dimension $1 + 1$ with an external forcing