19 citations · 61 across the 20 of their papers we have counts for
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Well-posedness and Hurst parameter estimation for fluid equations driven by fractional transport noise
Alexandra Blessing Neamtu, Dan Crisan, Oana Lang
We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter . The model capture…
A mild rough Gronwall Lemma with applications to non-autonomous evolution equations
Alexandra Blessing, Mazyar Ghani Varzaneh, Tim Seitz
We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs). This inequality together with an analysis of the C…
Existence of smooth stable manifolds for a class of parabolic SPDEs with fractional noise
Xiaofang Lin, Alexandra Neamtu, Caibin Zeng
Little seems to be known about the invariant manifolds for stochastic partial differential equations (SPDEs) driven by nonlinear multiplicative noise. Here we contribute to this as…
Bifurcation theory for SPDEs: finite-time Lyapunov exponents and amplitude equations
Dirk Blömker, Alexandra Neamtu
We consider a stochastic partial differential equation close to bifurcation of pitchfork type, where a one-dimensional space changes its stability. For finite-time Lyapunov exponen…
Stochastic evolution equations with rough boundary noise
Alexandra Neamtu, Tim Seitz
We investigate the pathwise well-posedness of stochastic evolution equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for $H\in(1/3,1/…
Quasilinear rough evolution equations
Antoine Hocquet, Alexandra Neamţu
We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt + F(u_t)\cdot d\mathbf X_t \), wh…
Center Manifolds for Rough Partial Differential Equations
Christian Kuehn, Alexandra Neamtu
We prove a center manifold theorem for rough partial differential equations (rough PDEs). The class of rough PDEs we consider contains as a key subclass reaction-diffusion equation…
Amplitude equations for SPDEs driven by fractional additive noise with small Hurst parameter
Dirk Blömker, Alexandra Neamtu
We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter . Close to a change of stability measured wi…
On the pitchfork bifurcation for the Chafee-Infante equation with additive noise
Alex Blumenthal, Maximilian Engel, Alexandra Neamtu
We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor i…
Global solutions for semilinear rough partial differential equations
Robert Hesse, Alexandra Neamtu
We construct global-in-time solutions for semilinear parabolic rough partial differential equations. We work on a scale of Banach spaces tailored to the controlled rough path appro…
On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs
Gaurav Dhariwal, Florian Huber, Alexandra Neamţu
The main goal of this work is to relate weak and pathwise mild solutions for parabolic quasilinear stochastic partial differential equations (SPDEs). Extending in a suitable way te…
Random attractors via pathwise mild solutions for stochastic parabolic evolution equations
Christian Kuehn, Alexandra Neamtu, Stefanie Sonner
We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In p…
Global martingale solutions for quasilinear SPDEs via the boundedness-by-entropy method
Gaurav Dhariwal, Florian Huber, Ansgar Jüngel +2
The existence of global-in-time bounded martingale solutions to a general class of cross-diffusion systems with multiplicative Stratonovich noise is proved. The equations describe…
Dynamics of Stochastic Reaction-Diffusion Equations
Christian Kuehn, Alexandra Neamtu
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-establis…
Random Attractors for Stochastic Partly Dissipative Systems
Christian Kuehn, Alexandra Neamtu, Anne Pein
We prove the existence of a global random attractor for a certain class of stochastic partly dissipative systems. These systems consist of a partial (PDE) and an ordinary different…
Sample Paths Estimates for Stochastic Fast-Slow Systems driven by Fractional Brownian Motion
Katharina Eichinger, Christian Kuehn, Alexandra Neamtu
We analyze the effect of additive fractional noise with Hurst parameter on fast-slow systems. Our strategy is based on sample paths estimates, similar to the appr…
Rough center manifolds
Christian Kuehn, Alexandra Neamtu
Since the breakthrough in rough paths theory for stochastic ordinary differential equations (SDEs), there has been a strong interest in investigating the rough differential equatio…
Global solutions and random dynamical systems for rough evolution equations
Robert Hesse, Alexandra Neamtu
We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and invest…
Local mild solutions for rough stochastic partial differential equations
Robert Hesse, Alexandra Neamtu
We investigate mild solutions for stochastic evolution equations driven by a fractional Brownian motion (fBm) with Hurst parameter H in (1/3, 1/2] in infinite-dimensional Banach sp…
Pathwise mild solutions for quasilinear stochastic partial differential equations
Christian Kuehn, Alexandra Neamtu
Stochastic partial differential equations (SPDEs) have become a key modelling tool in applications. Yet, there are many classes of SPDEs, where the existence and regularity theory…