Papers and Preprints

Book:

A.Boritchev, Sergei Kuksin, One-dimensional turbulence and the stochastic Burgers equation , Mathematical Surveys and Monographs vol. 255, AMS,
Link.

Articles and preprints:

1) A.Boritchev, Estimates for Solutions of a Low-Viscosity Kick-Forced Generalised Burgers Equation, Proceedings of the Royal Society of Edinburgh A, 143(2), 2013, 253-268.
Preprint. Final version.

2) A.Boritchev, Konstantin Khanin, On Hyperbolicity of Minimizers for 1D Random Lagrangian systems, Nonlinearity, 26, 1 (2013), 65-80.
Preprint. Final version.

3) A.Boritchev, Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation, Geometric and Functional Analysis, 23 (2013), 6, 1730-1771.
Preprint. Final version.

4) A.Boritchev, Decaying Turbulence in a Generalised Burgers Equation, Archive for Rational Mechanics and Analysis, 214 (2014), 1, 331-357.
Preprint. Final version.

5) A.Boritchev, Turbulence for the generalised Burgers Equation (review article), Russian Mathematical Surveys, 69:6(2014), 957-994.
Preprint. Final version.

6) A.Boritchev, Multidimensional potential Burgers turbulence, Communications in Mathematical Physics, 2016, 342:441.
Preprint. Final version.
Erratum, Communications in Mathematical Physics, 2016, 344:369.
Preprint. Final version.

7) A.Boritchev, Exponential convergence to the stationary measure for a class of 1D Lagrangian systems with random forcing, Stochastic and Partial Differential Equations : Analysis and Computation, 2018, 6 : 109-123.
Preprint. Final version.

8) A.Boritchev, Decaying turbulence for the fractional subcritical Burgers equation, Discrete and Continuous Dynamical Systems A, 2018, 38(5) : 2229-2249.
Preprint. Final version.

9) Piotr Biler, A.Boritchev, Grzegorz Karch, Philippe Laurençot, Concentration phenomena in a diffusive aggregation model, Journal of Differential Equations, 2021, 271: 1092-1108.
Preprint. Final version.

10) A.Boritchev, Daniel Eceizabarrena,  Victor Vilaça da Rocha, Intermittency of Riemann's non-differentiable function through the fourth-order flatness, Journal of Mathematical Physics, 62, 093101 (2021),
Preprint. Final version.

11) Piotr Biler, A.Boritchev, Grzegorz Karch,  Philippe Laurençot, Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation, Journal of Dynamics and Differential Equations, 2022, 34: 3131–3141, 
Preprint. Final version.

12) Piotr Biler, A.Boritchev, Lorenzo Brandolese, Latge Global Solutions of the parabolic Keller-Segel system in higher dimensions, 2023, 344: 891-914,  
Preprint.

13) Piotr Biler, A.Boritchev, Lorenzo Brandolese, Sharp well-posedness and blow-up results for parabolic systems of the Keller-Segel type,  
Preprint.

Proceedings:

1) A.Boritchev, 1D Burgers Turbulence: a model case for the Kolmogorov theory (in French), Laurent Schwartz seminar - PDE and applications (2011-2012), Exp. No. 40,
Preprint. Final version.

2) A.Boritchev, Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian systems, Proceedings of the Equadiff Conference 2017 (Bratislava),
Preprint. Final version.

Ph.D. thesis:

Defended on October 8, 2012 at Ecole Polytechnique: Generalised Burgers equation with random force and small viscosity.
Text of the thesis.
Slides shown at the Ph.D. defense.