**Lectures**

**Joachim Escher** (Gottfried Wilhelm Leibniz Universität Hannover, Germany)

Analytical aspects of thin film models with Marangoni effects

**Matthias Hieber** (TU Darmstadt, Germany)

Analytical aspects of geophysical flows

**Ansgar Juengel** (TU Wien, Austria)

Entropy dissipation methods for nonlinear PDEs

**Rico Zacher** (Martin-Luther-Universität Halle, Germany)

A priori estimates, regularity, and asymptotics for nonlocal in time PDEs

**Abstracts**

**Joachim Escher: Analytical aspects of thin film models with Marangoni effects **

1. Lubrication approximation including surface tension effects

2. Thin films as abstract evolution equations

3. Strong solutions and stability results

4. Regularizing, energy estimates, and global weak solutions

(Homepage of Joachim Escher)

**Matthias Hieber: Analytical aspects of geophysical flows**

1. Fluid Models arising in Geophysics: compressible/
incompressible flows, Boussinesq Approximation, stratified flows,
rotating fluids

2. The Stokes Operator: analytic semigroups, Helmholtz projection,
Kato-Iteration, Maximal Regularity

3. Boundary Layers: Stokes-Coriolis system, Ekman layers, stratified
flows, stability

4. Complex Fluids: Analysis of the MHD-system and Oldroyd-B fluids

(Homepage of Matthias Hieber)

**Ansgar Juengel: Entropy dissipation methods for nonlinear PDEs**

1. Motivation: heat equation and logarithmic entropy - some PDEs in
applications - what are these methods good for?

2. Entropy: definitions and examples - heat equation revisited -
the Boltzmann equation and the H-theorem

3. Fokker-Planck equations: long-time asymptotics of the heat equation
- logarithmic Sobolev inequalities - nonlinear Fokker-Planck equations
- the Bakry-Emery method

4. Further applications: symmetrization and entropies - construction
of entropies

(Homepage of Ansgar Juengel), (Script)

**Rico Zacher: A priori estimates, regularity, and asymptotics for nonlocal in time PDEs **

1. Nonlocal in time PDEs, in particular time fractional diffusion equations: applications in physics and mathematical approaches

2. Weak solutions in the subdiffusion case: energy estimates, Galerkin's method, boundedness, and the maximum
principle

3. Hölder and Harnack estimates for time fractional subdiffusion equations, global strong solvability of quasilinear
problems

4. Long-time behaviour: convergence to equilibrium, Lojasiewicz technique, and decay estimates

(Homepage of Rico Zacher)