@article{12486,
  abstract     = {This 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 Lp(Lq)-approach to stochastic PDEs, highlighting new connections between the two areas.},
  author       = {Agresti, Antonio},
  issn         = {2194-041X},
  journal      = {Stochastics and Partial Differential Equations: Analysis and Computations},
  publisher    = {Springer Nature},
  title        = {{Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations}},
  doi          = {10.1007/s40072-023-00319-4},
  year         = {2023},
}

@article{12178,
  abstract     = {In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L² regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well.},
  author       = {Agresti, Antonio and Hieber, Matthias and Hussein, Amru and Saal, Martin},
  issn         = {2194-041X},
  journal      = {Stochastics and Partial Differential Equations: Analysis and Computations},
  keywords     = {Applied Mathematics, Modeling and Simulation, Statistics and Probability},
  publisher    = {Springer Nature},
  title        = {{The stochastic primitive equations with transport noise and turbulent pressure}},
  doi          = {10.1007/s40072-022-00277-3},
  year         = {2022},
}

@article{9307,
  abstract     = {We establish finite time extinction with probability one for weak solutions of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t12) whereas the support of solutions to the deterministic PME grows only with rate O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong–Zakai type approximations, the transformation to a deterministic PME with two copies of a Brownian path as the lateral boundary, and techniques from the theory of viscosity solutions.},
  author       = {Hensel, Sebastian},
  issn         = {2194-041X},
  journal      = {Stochastics and Partial Differential Equations: Analysis and Computations},
  pages        = {892–939},
  publisher    = {Springer Nature},
  title        = {{Finite time extinction for the 1D stochastic porous medium equation with transport noise}},
  doi          = {10.1007/s40072-021-00188-9},
  volume       = {9},
  year         = {2021},
}