The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform
Stéphane Mischler - One of the best experts on this subject based on the ideXlab platform.
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uniqueness and long time asymptotic for the keller segel equation the parabolic elliptic case
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Giani Egana Fernandez, Stéphane MischlerAbstract:The present paper deals with the parabolic–elliptic Keller–Segel equation in the plane in the general framework of weak (or “free energy”) solutions associated to initial datum with finite mass M, finite second moment and finite entropy. The aim of the paper is threefold: (1) We prove the uniqueness of the “free energy” solution on the Maximal Interval of existence [0,T*) with T* = ∞ in the case when M ≦ 8π and T* 8π. The proof uses a DiPerna–Lions renormalizing argument which makes it possible to get the “optimal regularity” as well as an estimate of the difference of two possible solutions in the critical L4/3 Lebesgue norm similarly to the 2d vorticity Navier–Stokes equation. (2) We prove the immediate smoothing effect and, in the case M < 8π, we prove the Sobolev norm bound uniformly in time for the rescaled solution (corresponding to the self-similar variables). (3) In the case M < 8π, we also prove the weighted L4/3 linearized stability of the self-similar profile and then the universal optimal rate of convergence of the solution to the self-similar profile. The proof is mainly based on an argument of enlargement of the functional space for semigroup spectral gap.
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uniqueness and long time asymptotic for the parabolic parabolic keller segel equation the parabolic elliptic case
2016Co-Authors: Giani Egana Fernandez, Stéphane MischlerAbstract:The present paper deals with the parabolic–elliptic Keller–Segel equation in the plane in the general framework of weak (or “free energy”) solutions associated to initial datum with finite mass M, finite second moment and finite entropy. The aim of the paper is threefold: (1) We prove the uniqueness of the “free energy” solution on the Maximal Interval of existence [0,T*) with T* = ∞ in the case when M ≦ 8π and T* 8π. The proof uses a DiPerna–Lions renormalizing argument which makes it possible to get the “optimal regularity” as well as an estimate of the difference of two possible solutions in the critical L4/3 Lebesgue norm similarly to the 2d vorticity Navier–Stokes equation. (2) We prove the immediate smoothing effect and, in the case M < 8π, we prove the Sobolev norm bound uniformly in time for the rescaled solution (corresponding to the self-similar variables). (3) In the case M < 8π, we also prove the weighted L4/3 linearized stability of the self-similar profile and then the universal optimal rate of convergence of the solution to the self-similar profile. The proof is mainly based on an argument of enlargement of the functional space for semigroup spectral gap.
Giani Egana Fernandez - One of the best experts on this subject based on the ideXlab platform.
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uniqueness and long time asymptotic for the keller segel equation the parabolic elliptic case
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Giani Egana Fernandez, Stéphane MischlerAbstract:The present paper deals with the parabolic–elliptic Keller–Segel equation in the plane in the general framework of weak (or “free energy”) solutions associated to initial datum with finite mass M, finite second moment and finite entropy. The aim of the paper is threefold: (1) We prove the uniqueness of the “free energy” solution on the Maximal Interval of existence [0,T*) with T* = ∞ in the case when M ≦ 8π and T* 8π. The proof uses a DiPerna–Lions renormalizing argument which makes it possible to get the “optimal regularity” as well as an estimate of the difference of two possible solutions in the critical L4/3 Lebesgue norm similarly to the 2d vorticity Navier–Stokes equation. (2) We prove the immediate smoothing effect and, in the case M < 8π, we prove the Sobolev norm bound uniformly in time for the rescaled solution (corresponding to the self-similar variables). (3) In the case M < 8π, we also prove the weighted L4/3 linearized stability of the self-similar profile and then the universal optimal rate of convergence of the solution to the self-similar profile. The proof is mainly based on an argument of enlargement of the functional space for semigroup spectral gap.
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uniqueness and long time asymptotic for the parabolic parabolic keller segel equation the parabolic elliptic case
2016Co-Authors: Giani Egana Fernandez, Stéphane MischlerAbstract:The present paper deals with the parabolic–elliptic Keller–Segel equation in the plane in the general framework of weak (or “free energy”) solutions associated to initial datum with finite mass M, finite second moment and finite entropy. The aim of the paper is threefold: (1) We prove the uniqueness of the “free energy” solution on the Maximal Interval of existence [0,T*) with T* = ∞ in the case when M ≦ 8π and T* 8π. The proof uses a DiPerna–Lions renormalizing argument which makes it possible to get the “optimal regularity” as well as an estimate of the difference of two possible solutions in the critical L4/3 Lebesgue norm similarly to the 2d vorticity Navier–Stokes equation. (2) We prove the immediate smoothing effect and, in the case M < 8π, we prove the Sobolev norm bound uniformly in time for the rescaled solution (corresponding to the self-similar variables). (3) In the case M < 8π, we also prove the weighted L4/3 linearized stability of the self-similar profile and then the universal optimal rate of convergence of the solution to the self-similar profile. The proof is mainly based on an argument of enlargement of the functional space for semigroup spectral gap.
Dachun Yang - One of the best experts on this subject based on the ideXlab platform.
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Maximal function characterizations of hardy spaces associated to homogeneous higher order elliptic operators
Forum Mathematicum, 2016Co-Authors: Jun Cao, Svitlana Mayboroda, Dachun YangAbstract:Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and (q−(L), q+(L)) be the Maximal Interval of exponents q ∈ [1, ∞] such that the gradient semigroup { √ t∇e}t>0 is bounded on L(R). In this article, the authors establish the non-tangential Maximal function characterizations of the associated Hardy spaces H L(R) for all p ∈ (0, q+(L)), which, when p = 1, answers a question asked by Deng et al. in [J. Funct. Anal. 263 (2012), 604674]. Moreover, the authors characterize H L(R) via various versions of square functions and Lusin-area functions associated to the operator L.
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Maximal function characterizations of hardy spaces associated to homogeneous higher order elliptic operators
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Jun Cao, Svitlana Mayboroda, Dachun YangAbstract:Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and $(p_-(L),\, p_+(L))$ be the Maximal Interval of exponents $q\in[1,\,\infty]$ such that the semigroup $\{e^{-tL}\}_{t>0}$ is bounded on $L^q(\mathbb{R}^n)$. In this article, the authors establish the non-tangential Maximal function characterizations of the associated Hardy spaces $H_L^p(\mathbb{R}^n)$ for all $p\in(0,\,p_+(L))$, which, when $p=1$, answers a question asked by Deng et al. in [J. Funct. Anal. 263 (2012), 604-674]. Moreover, the authors characterize $H_L^p(\mathbb{R}^n)$ via various versions of square functions and Lusin-area functions associated to the operator $L$.
Keisho Katayama - One of the best experts on this subject based on the ideXlab platform.
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effects of Maximal Interval training on arterial oxygen desaturation and ventilation during heavy exercise
Japanese Journal of Physiology, 1999Co-Authors: Motohiko Miyachi, Keisho KatayamaAbstract:The purpose of the present study was to clarify longitudinally the effects of exercise training on arterial O(2) saturation (Sa(O(2))) and ventilation during heavy exercise. A group of six subjects (training group) volunteered to train four times a week for 12 weeks. Each training session consisted of five 3-min periods of exercise on a cycle ergometer at a power output of 100% Maximal O(2) uptake (V(.)(O(2 max))), interspersed with 2-min recovery period cycling at 50% V(.)(O(2 max)). During the training, V(.)(O(2 max)), Sa(O(2)), the ventilatory equivalent for oxygen (V(.)E/V(.)(O(2))), and the end-tidal partial pressure of O(2) (PET(O(2))) during heavy exercise were measured periodically. The same parameters were measured simultaneously in another group of five subjects (control group) who led normal lives. Maximal Interval training increases V(.)(O(2 max)), with little change in V(.)E(max) and pulmonary functions at rest. The training decreased PET(O(2)), V(.)E/V(.)(O(2)), and Sa(O(2)) during heavy exercise. Sa(O(2)) is significantly related to V(.)E/V(. )(O(2)) (r(2) = 0.49). These results suggest that less hyperventilatory response to exercise occurs with progress in physical training because the adaptability of ventilatory capacity is less than that of aerobic work capacity, which half induces arterial O(2) desaturation during heavy exercise. PET(O(2)) as well as V(.)E/V(.)(O(2)) and V(.)(O(2 max)) did not change anymore after the 6th week, nevertheless Sa(O(2)) kept decreasing up to the last 2 weeks. In addition, when the Sa(O(2))-V(.)E/V(.)(O(2)) plot was compared between the two groups, the regression line of the training group was steeper than that of the control groups; i.e., compared at a lower level of V(.)E/V(.)(O(2)) ( approximately 30 ml.ml(-1)), the Sa(O(2)) of the trained subjects exercising at a higher V(.)(O(2)) level was lower than that of the control subjects. Predominance of less hyperventilation and another factor, increased A-aDO(2), in the genesis of arterial hypoxemia and O(2) desaturation may be dependent upon V(.)(O(2)) levels in heavy exercise and the state of training.
Jun Cao - One of the best experts on this subject based on the ideXlab platform.
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Maximal function characterizations of hardy spaces associated to homogeneous higher order elliptic operators
Forum Mathematicum, 2016Co-Authors: Jun Cao, Svitlana Mayboroda, Dachun YangAbstract:Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and (q−(L), q+(L)) be the Maximal Interval of exponents q ∈ [1, ∞] such that the gradient semigroup { √ t∇e}t>0 is bounded on L(R). In this article, the authors establish the non-tangential Maximal function characterizations of the associated Hardy spaces H L(R) for all p ∈ (0, q+(L)), which, when p = 1, answers a question asked by Deng et al. in [J. Funct. Anal. 263 (2012), 604674]. Moreover, the authors characterize H L(R) via various versions of square functions and Lusin-area functions associated to the operator L.
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Maximal function characterizations of hardy spaces associated to homogeneous higher order elliptic operators
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Jun Cao, Svitlana Mayboroda, Dachun YangAbstract:Let $L$ be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and $(p_-(L),\, p_+(L))$ be the Maximal Interval of exponents $q\in[1,\,\infty]$ such that the semigroup $\{e^{-tL}\}_{t>0}$ is bounded on $L^q(\mathbb{R}^n)$. In this article, the authors establish the non-tangential Maximal function characterizations of the associated Hardy spaces $H_L^p(\mathbb{R}^n)$ for all $p\in(0,\,p_+(L))$, which, when $p=1$, answers a question asked by Deng et al. in [J. Funct. Anal. 263 (2012), 604-674]. Moreover, the authors characterize $H_L^p(\mathbb{R}^n)$ via various versions of square functions and Lusin-area functions associated to the operator $L$.