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# Documents  35B65 | enregistrements trouvés : 6

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## Post-edited  Singular SPDE with rough coefficients Otto, Felix (Auteur de la Conférence) | CIRM (Editeur )

We are interested in parabolic differential equations $(\partial_t-a\partial_x^2)u=f$ with a very irregular forcing $f$ and only mildly regular coefficients $a$. This is motivated by stochastic differential equations, where $f$ is random, and quasilinear equations, where $a$ is a (nonlinear) function of $u$.
Below a certain threshold for the regularity of $f$ and $a$ (on the Hölder scale), giving even a sense to this equation requires a renormalization. In the framework of the above setting, we present recent ideas from the area of stochastic differential equations (Lyons' rough path, Gubinelli's controlled rough paths, Hairer's regularity structures) that allow to build a solution theory. We make a connection with Safonov's approach to Schauder theory.
This is based on joint work with H. Weber, J. Sauer, and S. Smith.
We are interested in parabolic differential equations $(\partial_t-a\partial_x^2)u=f$ with a very irregular forcing $f$ and only mildly regular coefficients $a$. This is motivated by stochastic differential equations, where $f$ is random, and quasilinear equations, where $a$ is a (nonlinear) function of $u$.
Below a certain threshold for the regularity of $f$ and $a$ (on the Hölder scale), giving even a sense to this equation requires a ...

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## Virtualconference  A new commutator method for averaging lemmas (part 1) Jabin, Pierre-Emmanuel (Auteur de la Conférence) | CIRM (Editeur )

This talk introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. The new method outperforms classical averaging lemma results when the right-hand side of the kinetic equation has enough integrability. It also allows a perturbative approach to averaging lemmas which provides, for the first time, explicit regularity results for non-homogeneous velocity fluxes.
This talk introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. The new method outperforms classical averaging lemma results when the right-hand side of the ...

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## Virtualconference  A new commutator method for averaging lemmas (part 2) Jabin, Pierre-Emmanuel (Auteur de la Conférence) | CIRM (Editeur )

This talk introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. The new method outperforms classical averaging lemma results when the right-hand side of the kinetic equation has enough integrability. It also allows a perturbative approach to averaging lemmas which provides, for the first time, explicit regularity results for non-homogeneous velocity fluxes.
This talk introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. The new method outperforms classical averaging lemma results when the right-hand side of the ...

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## Virtualconference  A new commutator method for averaging lemmas (part 3) Jabin, Pierre-Emmanuel (Auteur de la Conférence) | CIRM (Editeur )

This talk introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. The new method outperforms classical averaging lemma results when the right-hand side of the kinetic equation has enough integrability. It also allows a perturbative approach to averaging lemmas which provides, for the first time, explicit regularity results for non-homogeneous velocity fluxes.
This talk introduces, in a simplified setting, a novel commutator method to obtain averaging lemma estimates. Averaging lemmas are a type regularizing effect on averages in velocity of solutions to kinetic equations. We introduce a new bilinear approach that naturally leads to velocity averages in $L^{2}\left ( \left [ 0,T \right ],H_{x}^{s} \right )$. The new method outperforms classical averaging lemma results when the right-hand side of the ...

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## Virtualconference  Quantitative De Giorgi methods in kinetic theory Mouhot, Clément (Auteur de la Conférence) | CIRM (Editeur )

We consider hypoelliptic equations of kinetic Fokker-Planck type, also sometimes called of Kolmogorov or Langevin type, with rough coefficients in the drift-diffusion operator in velocity. We present novel short quantitative proofs of the De Giorgi intermediate-value Lemma as well as weak Harnack and Harnack inequalities (which imply Hölder continuity with quantitative estimates).
This is a joint work with Jessica Guerand.

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## Virtualconference  Partial regularity in time for the Landau equation with Coulomb interaction Golse, François (Auteur de la Conférence) | CIRM (Editeur )

Whether there is global regularity or finite time blow-up for the space homogeneous Landau equation with Coulomb potential is a longstanding open problem in the mathematical analysis of kinetic models. This talk shows that the Hausdorff dimension of the set of singular times of the global weak solutions obtained by Villanis procedure is at most 1/2.
(Work in collaboration with M.P. Gualdani, C. Imbert and A. Vasseur)

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