guacho
Reputation
409
Next privilege 500 Rep.
Access review queues
 Feb 1 comment Smoluchowski-Poisson dynamics with atomic measures For the parabolic-elliptic Keller-Segel eq there are results concerning measure valued solutions ceremade.dauphine.fr/~dolbeaul/Preprints/Fichiers/DolbSchm.pdf Jan 4 asked Constant periodic Sobolev embedding Nov 1 awarded Yearling Nov 1 answered Asking for Advices for Choosing a Ph.D thesis problem (in PDE area) May 17 awarded Critic May 8 awarded Curious Apr 29 comment Boundedness of heat semigroup on $L^1(\Omega)$ For positive $f$ and neumann BC for the laplacian, you can prove the conservation of the $L^1$ norm by using the divergence theorem. Apr 14 accepted Mathematical difference between entropy and energy Apr 14 comment Mathematical difference between entropy and energy where can I see this computation? Can you give me a reference? Apr 14 awarded Nice Question Apr 13 comment Mathematical difference between entropy and energy Thank you for your comment. I already knew about the term "free energy". There is another question arising here: what is the difference between and energy and a free energy? Apr 13 comment Mathematical difference between entropy and energy Thank you for your answer! Actually, there are examples where $H$ does not decay (for instance, the parabolic-elliptic) Keller-Segel. Also, I would say that the regularity to preserve $L^2$ for the Euler flow and the regularity to preserve $LlogL$ is the same, $C^{1/3}$. Isn't it? With this I meant that there should be something else, not merely the monotonicity or well-behaviour. Am I right? Apr 13 comment Mathematical difference between entropy and energy Thank you for your answer! I was assuming $u_0$, to be positive, so there was no problem on difining the entropy. Why do you say the case $2=p$ is the usual energy inequality? Maybe is a stupid question, but, even if I see that this quotient has the same flavour, I don't see why it's the same thing. Apr 13 asked Mathematical difference between entropy and energy Mar 18 comment Schauder estimate on a bounded domain Mmm, I don't see how that can be true. Take $u$ the solution to $$\Delta u=0 \text{ in }U$$ and $$u=g(x,y) \text{ on }\partial U$$. Here $g$ is a smooth function. Then the right hand side vanishes, but the function $u$ is not necessarily constant. Oct 13 accepted Relationship between LlogL and Hardy spaces Oct 13 revised Relationship between LlogL and Hardy spaces edited tags Oct 13 asked Relationship between LlogL and Hardy spaces Sep 1 comment Interpolation between L^1 and Sobolev Space It is a very interesting question. Maybe a good start point is Lemma 5.3 in arxiv.org/pdf/1104.0306.pdf and Lemma 6.6 in arxiv.org/pdf/0812.4979v1.pdf I would also suggest to think on homogeneous Sobolev spaces, the embeding operator and the Riesz-Thorin Theorem. Jun 5 accepted A bound in Sobolev spaces of negative order