Abstract
AbstractThis paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the $$L^p(L^q)$$
L
p
(
L
q
)
-approach to stochastic PDEs, highlighting new connections between the two areas.
Funder
European Research Council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Modeling and Simulation,Statistics and Probability
Reference74 articles.
1. Agresti, A., Lindemulder, N., Veraar, M.C.: On the trace embedding and its applications to evolution equations. Math. Nachr. 296(4), 1319–1350 (2023)
2. Agresti, A., Veraar, M.C.: Stability properties of stochastic maximal $$L^p$$-regularity. J. Math. Anal. Appl. 482(2), 123553 (2020)
3. Agresti, A., Veraar, M.C.: Stochastic maximal $${L}^p({L}^q)$$-regularity for second order systems with periodic boundary conditions. arXiv preprint arXiv:2106.01274, 2021. To appear in Annales de l’Institut Henri Poincaré (B) Probability and Statistics
4. Agresti, A., Veraar, M.C.: Stochastic Navier–Stokes equations for turbulent flows in critical spaces. arXiv preprint arXiv:2107.03953 (2021)
5. Agresti, A., Veraar, M.C.: Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity 35(8), 4100 (2022)
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献