122 records found

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## Authored

## Reaction-diffusion equations with transport noise and critical superlinear diffusion

### Global well-posedness of weakly dissipative systems

In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the d-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g., the Allen-Cahn equation) and dissipative systems (e.g., ...

## Reaction-diffusion equations with transport noise and critical superlinear diffusion

### Global well-posedness of weakly dissipative systems

In this paper, we investigate the global well-posedness of reaction-diffusion systems with transport noise on the d-dimensional torus. We show new global well-posedness results for a large class of scalar equations (e.g., the Allen-Cahn equation) and dissipative systems (e.g., ...

## Reaction-diffusion equations with transport noise and critical superlinear diffusion

### Local well-posedness and positivity

In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of high ...

## Analysis in Banach Spaces

### Volume III. Harmonic Analysis and Spectral Theory

In this chapter, we complement the discussion of three major themes of Fourier analysis that we have studied in the previous Volumes.

@enThis chapter presents an in-depth study of several classes of vector-valued function spaces defined by smoothness conditions.

@enIn this chapter we address a couple of topics in the theory of H^{∞}-calculus centering around the question what can be said about an operator of the form A+B when A and B have certain “good” properties such as being (R-)sectorial or admitting a bounded H^{∞}-c
...

In this chapter we address two strongly interwoven topics: How to verify the boundedness of the H^{∞}-calculus of an operator and how to represent and estimate its fractional powers. For concrete operators such as the Laplace operator or elliptic partial differential o
...

Before addressing this question for the Calderón{Zygmund type operators of the kind studied in Chapter 11, we investigate a number of related objects in a simpler dyadic model. Besides serving as an introduction to some of the key techniques, it turns out that these dyadic ope ...

The mapping properties of T will of course heavily depend on the assumptions made on the kernel K that we will discuss in more detail in this chapter.

@enAs we have seen in the preceding sections, in the context of inhomogeneous linear evolution equations, maximal regularity enables one to set up an isomorphism between the space of data (initial value and inhomogeneity) and the solution space.

@en## Nonlinear parabolic stochastic evolution equations in critical spaces part II

### Blow-up criteria and instantaneous regularization

This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinear ...